College of Engineering : [catalog]. · 122/AEROSPACEENGINEERING AerospaceEngineering DepartmentOffice:302AerospaceEngineeringBuilding,phone(313)764-3310 SeePage121forstatementonCourseEquivalence.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:0

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

03

02

49

94

3O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

College of Engineering : [catalog].University of Michigan.Ann Arbor, Mich. : The University of Michigan,

http://hdl.handle.net/2027/mdp.39015030249943

Open Access, Google-digitizedhttp://www.hathitrust.org/access_use#oa-google

This work is protected by copyright law (which includescertain exceptions to the rights of the copyright holderthat users may make, such as fair use where applicableunder U.S. law). It is made available from HathiTrustwith permission of the copyright holder. Permissionmust be requested from the rights holder for any subsequentuse. The digital images and OCR of this work were producedby Google, Inc. (indicated by a watermark on each pagein thePageTurner). Google requests that these imagesand OCR not be re-hosted, redistributed or used commercially.They are provided for educational, scholarly, non-commercialpurposes.

122 / AEROSPACE ENGINEERING

Aerospace Engineering

Department Office: 302 Aerospace Engineering Building, phone (313) 764-3310

See Page 121 for statement on Course Equivalence.

100. Introduction to Flight. (2).An introduction to the physical principles of flight within the atmosphere and in space, to the majorhistorical developments in the conquest of air and space, and to the current state of aerospace

developments and their role in national and world affairs.

200. General Aeronautics and Astronautics. Prerequisite: Physics 140. preceded or accompanied by Eng. 102. I and II. (2).

Introduction to aerospace engineering. Elementary' problems designed to orient the student in the

program of aerospace engineering, together with a discussion of the current state of aerospacedevelopments and the role of the engineer. Recitations and demonstrations.

300. Elements of Space Science and Technology. Prerequisite: Math. 216; Physics 240. (3).Scientific and technological aspects of current space flights, mission goals, the space environment,

vehicle characteristics, performance, and flight paths. Mission support: communications, power,computers, etc. Open to all University students.

301. Laboratory I. Prerequisite: preceded or accompanied b\ Elec.-Comp. Eng. 314. I and II.(2).

Comprehensive series of lectures and experiments designed to introduce the student to basic

principles of electronics, circuit analysis, transducers, modem laboratory instrumentation, experimental methods, and data analysis. Experiments involve simple measurement and instrumentation

problems.

302. Laboratory II. Prerequisite: Aero. Eng. 301 . I and II. (2).Continuation of the material in Aero. Eng. 301.

3l4(Appl. Mech. 314). Structural Mechanics I. Prerequisite: Appl. Mech. 211 . I and II. (3).Review of plane states of stress and strain. Basic equations of plane elasticity and selected problems:failure criteria and applications; energy principles of structural theory: thin-walled beam theory.

320. Compressible Flow and Propulsion I. Prerequisite: Mech. Eng. 235. I and II. (3).First part of an aerodynamics sequence designed to study the fundamental principles and their

applications: physical nature of fluids, conservation laws; nozzles and diffusers; shock waves;

applications to jet propulsion and other problems.

330. Aerodynamics II. Prerequisite: Aero. Eng. 320 or introductory course in fluid mechanics. I

and II. (3).Second part of an aerodynamics sequence designed to study the fundamental principles and their

applications; viscous effects in laminar and turbulent flows; boundary layer theory; concepts of

instability and transition to turbulent flow; flows under the influence of gravitational and electromagnetic

forces.

340. Mechanics of Flight. Prerequisite: Aero. Eng. 200, Appl. Mech. 240. I and II. (3).Mechanics of a particle applied to the analysis of vehicle flight paths. Rigid body mechanics applied

to translational and rotational vehicle motion. Analysis of vehicle motion and static and dynamic

stability using perturbation theory.

350(Math. 350). Aerospace Engineering Analysis. Prerequisite: Math. 216. I and II. (3).Formulation and solution of some of the elementary initial- and boundary-value problems relevant to

aerospace engineering. Application of Fourier series, separation of variables, and vector analysis to

problems of forced oscillations, wave motion, diffusion, elasticity, and perfect-fluid theory.

380. Undergraduate Seminar. Prerequisite: junior standing. (1 ).

A series of seminars by noted outside speakers designed to acquaint undergraduates with both current

problems and state of the art of the aerospace industry. Will involve a short term project or paper

pertinent to one of the seminar topics.

390. Directed Study. (To be arranged).Individual study of specialized aspects of aerospace engineering.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:0

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

03

02

49

94

3O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

AEROSPACE ENGINEERING I 123

411(Appl. Mech. 411)(Civ. Eng. 411KNav. Arch. 411). Finite Element Applications. Prerequisite:

Eng. 102, Appl. Mech. 211. I. (3).The application of user oriented finite element computer programs for solving practical structural

mechanics problems of frames, 2-D and 3-D solids, plates, shells, etc., and displaying the solutions

graphically. Students learn to prepare input data and interpret results. A short introduction to the

underlying theory is also presented.

414(Appl. Mech. 414). Structural Mechanics II. Prerequisite: Aero. Eng. 314. I and II. (3).Introduction to plate theory. Stability of structural elements; columns and beam columns; plate in

compression and shear; secondary instability of columns. Introduction to matrix methods of deforma

tion analysis; structural dynamics.

420. Aerodynamics III. Prerequisite: Aero. Eng. 320, and Aero. Eng. 350 or Math. 450. I and

II. (3).Third part of an aerodynamic sequence designed to study the fundamental principles and their

applications; inviscid flows and fundamentals of field theory; generation of airfoil lift; thin airfoil

theory; induced drag and finite wings; wave kinematics; two dimensional compressible flow.

423. Aero-Acoustics. Prerequisite: Aero. Eng. 320 or a course in compressible flow. (3).

Principles of generation, perception, and abatement of sound generated by fluid flows. Elementaryacoustics; acoustical response of the human ear. Theory and results of measurement of sound

generated by explosions, sonic booms, jets, boundary layers, and flow excited structural vibrations.

Qualitative assessment of techniques and effectiveness of noise abatement procedures.

430. Propulsion II. Prerequisite: Aero. Eng. 320. I and II. (3).Performance and analysis of flight-propulsion systems including the reciprocating engine-propeller,

turbojet, turboprop, ramjet, and rocket.

433. Combustion Processes. Prerequisite: Aero. Eng. 320. (3).

Study of combustion processes with appropriate consideration of the fluid mechanics (aero-thermo

chemistry); emphasis placed on the physical understanding, applications, performance, pollution

aspects, experimental techniques, and commonality between jet propulsion combustors, internal

combustion engines, and stationary power plants; includes equilibrium constants, chemical kinetics,

flames, explosions, liquid drops, particulate formation.

439. Aircraft Propulsion Laboratory. Prerequisite: Aero. Eng. 320. (2).Series of experiments designed to illustrate the general principles of propulsion and to introduce the

student to certain experimental techniques in the study of actual propulsive devices, using full-scale

or reduced models of the pulsejet, turbojet, ramjet, and rocket motors.

440. Vehicle Systems Performance. Prerequisite: junior standing. (3).Role of performance in systems analysis; mathematical modeling; identification of constraints,

performance parameters, and performance indices. The aircraft performance problem: flight enve

lope, aerodynamic approximations, available propulsion systems; takeoff, landing, climb, and range

performance. Modern performance optimization techniques. Applications to automobile, high-speedtrain, and space vehicle performance analysis.

447. Flight Testing. Prerequisite: Aero. Eng. 340. (2).Theory and practice of obtaining flight-test data on performance and stability of airplanes from actual

flight tests. No laboratory fee will be charged, but a deposit covering student insurance and operating

expense of the airplane will be required.

449. Principles of Vertical Take-off and Landing Aircraft. Prerequisite: Aero. Eng. 420. (3).Lifting rotor and propellor analysis in vertical and forward flight; ducted fan analysis; helicopter

performance analysis; transitional flight problems of VTOL aircraft; stability and control problems ofhelicopters and VTOL aircraft.

452(C.I.C.E. 412) (Elec.-Comp. Eng. 412). Engineering Probability and Statistics. Prerequisite:Math. 215. I and II. (3).

Basic concepts of probability theory; random variables, probability distributions, averages, mo

ments, characteristic functions, independence. Binomial, Poisson, and Gaussian distributions. Intro

duction to statistical inference and its applications in engineering, statistics of measurements,

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:0

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

03

02

49

94

3O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


confidence intervals, least square fitting of data. C.I.C.E. students may not receive graduate credii

for both C.I.C.E. 412 and C.I.C.E. 512.

454(C.I.C.E. 482) (Elec.-Comp. Eng. 482). Analog Computation. Prerequisite: Math. 216. (3).

Basic theory of analog computers. Analog devices; operational amplifiers, multipliers, function

generators. Analog simulation of linear and nonlinear dynamic systems, including ordinary and

partial differential equations. Lecture and laboratory.

455(C.I.C.E. 465) (Elec.-Comp. Eng. 465). Computer Graphics Application. PrerequisiteElec.-Comp. Eng. 270 or I.&O.E. 473 or Comp. <S Comm. Sci. 374 or C.I.C.E. 461. (3).

Application of several software packages and display devices for engineering problem solving and

production of computer animated films. Use of Computek. Tektronix, and PDP graphics terminals

for electrical circuit design, interactive data smoothing, production of engineering graphs, etc.

POLYGRAPHICS and BEFLIX computer animation packages and their use in MTS. Production of 2

or 3 films using graphics terminals.

464(A.&O.Sci. 464). Upper Atmospheric Science. Prerequisite: senior or graduate standing in

a physical science or engineering. I. (3).An introduction to physical processes in the upper atmosphere; density, temperature, composition,and winds; atmospheric radiation transfer processes and heat balance: the ionosphere; rocket and

satellite measurement techniques.

465(A.&0. Sci. 465). Atmospheric Measurements and Data Analysis. Prerequisite: senior or

graduate standing in a physical science or engineering. II. (3).Introduction to operational and experimental measurements of atmospheric parameters. Instrumenta

tion for "in-situ" measurements at the surface and from aerospace vehicles. Remote sensing using

electromagnetic radiation and acoustical waves with both passive and active systems. Analysis of

data, error theory, the use of least squares methods and empirical orthogonal functions, the informa

tion content of experimental data.

471. Automatic Control Systems. Prerequisite: Math, 216. I and II. (3).Transient and steady-state analysis of linear control systems; transfer function and state-space

description of control systems; stability analysis and synthesis methods; application to the design of

autopilots and other modem control systems; introduction to nonlinear control systems and phase

plane analysis.

472(C.I.C.E. 450) (Elec.-Comp. Eng. 450). Fundamentals of Control Systems. Prerequisite:

Appl. Mech. 240. Elec.-Comp. Eng. 310, or Elec-Comp, Eng. 355, and senior standing . I and

n. (3).Concept and importance of control systems. Control system descriptions: state variable and transfer

function representations. System performance and design criteria: stability, sensitivity, time response.

Concept of feedback. Time response of linear control systems. Use of Hurwitz, root-locus, Nyquistand Bode methods for analysis and synthesis of linear control systems. Not open to students with

credit for Aero. Eng. 471.

473(C.I.C.E. 451) (Elec.-Comp. Eng. 451). Control Systems Laboratory . Prerequisite: CV.Cf.450 or Aero. Eng. 471. (2).

Introduction to control system simulation and design. Experiments with physical systems. Illustrationof basic control principles. Design examples and the use of computer design aids.

481. Airplane Design. Prerequisite: senior standing. I. (4).Power-required and power-available characteristics of aircraft on a comparative basis, calculation of

preliminary performance, stability, and control characteristics. Design procedure, including layouts

and preliminary structural design. Subsonic and supersonic designs. Emphasis on design techniques

and systems approach. Lectures and laboratory.

482. Design of Rocket- and Air-Borne Remote Sensing Probes. Prerequisite: senior standing.

(4).Design techniques and projects for geophysical, environmental, and earth resources surveys. Aircraft, sounding rocket, and balloon instruments and payloads as well as vehicle characteristics, and

performance are considered. Student projects bring together in a unified concept components for

sensing (remote and in situ), telemetering, tracking, performance, safety, and data processing.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:0

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

03

02

49

94

3O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


483. Aerospace System Design. Prerequisite: senior standing. II. (4).Aerospace system design, analysis and integration. Consideration of launch facilities, booster

systems, spacecraft systems, communications, data processing, and project management. Lectures

and laboratory.

485(C.I.C.E. 435) (Elec.-Comp. Eng. 435). Aerospace Communication Systems. Prerequisite:

Math. 450 or Aero. Eng. 350. Elec.-Comp. Eng. 314. (3).Introduction to the design of space communications and tracking systems for the aerospace system

designer. Basic principles in the design of space communications and tracking systems, including

modulation-demodulation techniques, frequency and time division multiplexing, methods of data

storage, system gain considerations, power sources, antennas, propagation, and tracking methods.

Application to system problems emphasized.

490. Directed Study. (To be arranged).Individual study of specialized aspects of aerospace engineering. Primarily for undergraduates.

510(Appl. Mech. 510)(Mech. Eng. 557). Finite Element Methods in Mechanics I. Prerequisite:Aero. Eng. 414(Appl. Mech. 414) or Mech. Eng. 362. I. (3).

Development of the finite element method with emphasis on energy principles. Virtual work.

Potential energy. Application to line elements, beams, plane stress, plane strain, and three-

dimensional stress. Several computer problems assigned.

514(Appl. Mech. 514). Foundations of Structural Mechanics I. Prerequisite: Aero. Eng. 414.

(3).Elements of the analysis of structures. Includes plates of various shapes, loading and boundaryconditions, effects of in-plane loading; shells of revolution, cylindrical shells, bending and membrane theories; plastic analysis of structures, beams, frames, plates; plastic collapse mechanism.

Applications of aerospace interest.

515(Appl. Mech. 515). Foundations of Structural Mechanics II. Prerequisite: Aero. Eng. 514.

(3).Behavior of structures in a thermal environment, heat conduction, aerodynamic heating of high speed

vehicles, thermal stresses and deflections, thermal instabilities, discussion of material properties at

elevated temperature. Elements of the theory of linear viscoelasticity.

520. Gasdynamics I. Prerequisite: Aero. Eng. 420 or 425. (3).Gasdynamics at an intermediate level: Thermodynamics; the conservation equations; vorticity theorems;

unsteady one-dimensional flow; the method of characteristics; stationary and moving shock waves;

two-dimensional steady flow including method of small perturbations.

521. Experimental Gasdynamics. Prerequisite: Aero. Eng. 330 and 420. (3).Experimental methods in modern gasdynamics; physical principles and interpretation. Shop practiceand theory of instrument design: mechanics, electronics, and optics. Measurement of velocity,

pressure, density, temperature, composition, energy and mass transfer in fluids and plasmas.Transducers and laboratory instrumentation in gasdynamic research.

522. Gasdynamics II. Prerequisite: Aero. Eng. 520. (3).The Navier-Stokes equations, including elementary discussion of tensors; exact solutions. Laminar

boundary-layer theory; asymptotic concepts; solutions for incompressible boundary layers. Compressible boundary layers; special solutions; transformation of equations; heat transfer in forced and free

convection. Introduction to the mechanics of turbulence; Reynolds stresses; turbulent boundary

layers.

529. Introduction to Energy Transfer. Prerequisite: Aero. Eng. 330. (3).A survey of energy transfer processes including unsteady heat conduction, convection in non-reactiveand reactive flows, and radiation. Aerospace applications, including re-entry heating, ablation,

rocket nozzle cooling, radiative transfer, satellite heating, convection in dissociated flows.

530. Propulsion III. Prerequisite: Aero. Eng. 430. (3).Continuation of Aero. Eng. 430. Further treatment of aircraft engine performance, including

off-design operation, and study of selected problems in the field of propulsion.

532. Introduction to Gaskinetics and Real Gas Effects. Prerequisite: Aero. Eng. 420. (3).A study of some modem topics of flow problems not covered in the traditional gasdynamics of ideal

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:0

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

03

02

49

94

3O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


gases: concepts of gaskinetics, aerodynamics of free molecules, shock transition layer, real gaseffects, high temperature effects, multicomponent flows, etc.

535. Rocket Propulsion. Prerequisite: Aero. Eng. 430 or 435. (3).Analysis and performance of liquid and solid propellant rocket powerplants; propellant thermochemistry .

heat transfer, system considerations, advanced rocket propulsion techniques.

540(Appl. Mech. 540). Intermediate Dynamics. Prerequisite: Appl. Mech. 240. I. (4).Kinematics of motion, particle dynamics. Lagrange's equations. Rigid body dynamics includingEuler's equations, the Poinsot construction, spin stabilization, the rotation matrix. Vibrations ofcoupled systems, orthogonality relationships, generalized co-ordinates and generalized system parameters.

542. Astrodynamics I. Prerequisite: Aero. Eng. 340. I. (3).The study of motion of spacecraft in a vacuum and in the atmosphere with emphasis on preliminarymission planning. Analysis of trajectories in suborbital, orbital, lunar, and interplanetary operations.

Aerodynamic forces and heating characteristics and their effect on the selection of flight paths during

entry into planetary atmospheres.

543. Structural Dynamics. Prerequisite: Aero. Eng. 414 or 540. (3).Natural frequencies and mode shapes of elastic bodies. Nonconservative elastic systems. Structural

and viscous damping. Influence coefficient methods for typical flight structures. Response ofstructures to random and shock loads. Lab demonstration.

544. Aeroelasticity. Prerequisite: Aero. Eng. 414 or 540. (3).An introduction to aeroelasticity. Vibration and flutter of elastic bodies exposed to fluid flow. Static

divergence and flutter of airplane wings. Flutter of flat plates and thin walled cylinders at supersonic

speeds. Oscillations of structures due to vortex shedding.

546. Advanced Dynamics. Prerequisite: Aero. Eng. 540. (3).Hamilton's equations, canonical transformations, and Hamilton-Jacobi theory. Applications to orbital

problems. General perturbation theory. Introduction to special relativity.

548. Astrodynamics II. Prerequisite: Aero. Eng. 542. (3).Orbit determination. Systems of canonical equations. Perturbation theory with applications to the

motion of an artificial satellite. Lunar and planetary theories.

549(Appl. Mech. 549) (Mech. Eng. 549). Random Vibrations of Mechanical Systems.

Prerequisite: Appl. Mech. 240. (3).Random mechanical inputs; wind buffeting; earthquakes; surface irregularities. Engineering applications include response of linear spring-mass system and an elastic beam to single and mutiple random

loading. Failure theories. Necessary concepts such as ensemble averages, correlation functions,

stationary and ergodic random processes, power spectra, are developed heuristically.

570. Guidance and Navigation of Aerospace Vehicles. Prerequisite: a course in feedback con

trol. I. (3).Principles of space vehicle, homing and ballistic missiles guidance systems in two and three

dimensions. Explicit, linear perturbation, and velocity-to-be gained guidance modes. Mechanization

by inertial and other means, including strapped-down and stable-platform inertia! systems. Celestial

navigation procedures with deterministic and redundant measurements. Application of Kalman

filtering to recursive navigation theory.

574. Control of Aircraft, Missiles, and Space Vehicles. Prerequisite: preceded or accompaniedby C.I.C.E. 550. II. (2).

Analysis and synthesis of autopilots for aircraft and cruise-type missiles. Design of thrust- vector

control systems including effects of elastic structures and fuel sloshing. Attitude control systems for

space vehicles; mechanization using jet thrusters and inertia wheels; gravity gradient moments

575. Optimization of Space Trajectories. Prerequisite: permission of instructor. U. (3).Necessary and sufficient conditions for ordinary extremum and variational problems, with emphasison the problem of Bolza. Applications of the calculus of variations to optimal space trajectoriesProblems with control and state variable inequality constraints. Iterative computational methods for

two-point boundary-value problems, including the gradient method. Newton's method, andquasilinearization.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:0

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

03

02

49

94

3O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


590. Directed Study. (To be arranged).Individual study of specialized aspects of aerospace engineering. Primarily for graduates.

596. Aurora and Airglow. Prerequisite: permission of instructor. II. (3).Morphology and physics of the aurora and airglow. Emission spectra in the aurora and their atomic

and molecular origin; proton aurora; metastable excitation; calculation of emission profiles. Night-

and day-glow; pre-dawn and post-twilight enhancements; mid-latitude red arc; excitation mecha

nisms.

610(Appl. Mech. 610). Finite Element Methods in Mechanics II. Prerequisite: Aero. Eng.

510(Appl. Mech. 510) (Mech. Eng. 557). II. (3).Advanced topics in finite element theory. Plates, shells, large deflections, stability, plasticity,

dynamics. Iterative methods for nonlinear problems. Solution of field problems for fluid flow and

electric potential. Survey of software available.

620. Dynamics of Viscous Fluids. Prerequisite: Aero. Eng. 520. (3).Navier-Stokes equations; low Reynolds number flows; incompressible and compressible laminar

boundary layers; boundary layer stability and transition to turbulence; turbulent boundary layers,wakes, and jets.

621. Dynamics of Compressible Fluids. Prerequisite: Aero. Eng. 520. (3).Theory of characteristics; shock-wave phenomena; interaction problems; hodograph transformation;

transonic flow.

627. Continuum Theory of Fluids. Prerequisite: Aero. Eng. 520. (3).Physical concepts underlying the flow of fluids acted upon by stresses arising from viscosity and from

electromagnetic and gravity fields. Invariant analysis of stress-strain relations. Maxwell's equations,

analysis of electromagnetic stresses and energy dissipation in moving media, the equations of motion

and energy in a moving fluid, and some solutions of the complete equations.

628. Statistical Theory of Fluids. Prerequisite: Aero. Eng. 532. (3).A study of the flows of neutral and charged particles from the viewpoint of kinetic theory;

Chapman-Enskog theory of transport phenomena, dynamics of rarefied gases, plasma kinetics

without external magnetic field, plasma oscillations and Landau damping, microinstabilities, plasma

interactions.

632. Gas Flows with Chemical Reactions. Prerequisite: Aero. Eng. 532, 620. (3).Thermodynamics of gas mixtures, chemical kinetics, conservation equations for multicomponent

reacting gas mixtures. Deflagration and detonation waves. Nozzle flows and boundary layers with

reaction and diffusion.

673(FJec.-Comp. Eng. 673) (Nuc. Eng. 673). Topics in Theoretical Plasma Physics. Prerequisite:

Nuc. Eng. 571 or Elec.-Comp. 580 or Aero. Eng. 726. I and II. (3). This course may be taken

for credit more than once.

An advanced course in theoretical plasma physics covering topics of current research interest.

Specific content will vary from year to year. Representative topics include: studies of weakly ionized

plasmas with applications to gas lasers; space plasmas; laser fusion plasmas; and nonlinear plasma

dynamics and plasma turbulence.

721. Turbulence. Prerequisite: Aero. Eng. 620. (3).Physical and mathematical description of turbulence in boundary layers, wakes, jets, and behind

grids, turbulent fields; theories for turbulent mass, momentum, heat, and particle diffusion.

726. Introduction to Plasma Dynamics. Prerequisite: permission of instructor. (3).Physical properties of a plasma: particle orbit theory; collective phenomena in a plasma; kinetic

equations for a plasma; instabilities; transport phenomena and derivation of the magnetohydrodynamic

equations. •

729. Special Topics in Gasdynamics. Prerequisite: permission of instructor. (To be arranged).

Advanced topics of current interest.

800. Seminar. (To be arranged).

810. Seminar in Structures. (To be arranged).

820. Seminar in Aerodynamics. (To be arranged).

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:0

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

03

02

49

94

3O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


830. Seminar in Propulsion. (To be arranged).

840. Seminar in Mechanics of Flight. (To be arranged).

880. Seminar in Space Technology. Prerequisite: permission of instructor. (To be arranged).

990. Dissertation Pre-Candidate. I and II (2-8); IIIa and III* (1-4).Election for dissertation work by doctoral student not yet admitted to status as a Candidate.

995. Dissertation/Candidate. Prerequisite: Graduate School authorization for admission as a

doctoral candidate. I and II (8); IIIa and Ulb (4).Election for dissertation work by doctoral student who has been admitted to status as a Candidate

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:0

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

03

02

49

94

3O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:1

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

44

5O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle





l24 / AEROSPACE ENGINEERING


Department Office: 302 Aerospace Engineering Building, phone (3l3) 764-33l0

See Page l23 for statement on Course Equivalence.

100. Introduction to Flight. (2).An introduction to the physical principles of flight within the atmosphere and in space, to the majorhistorical developments in the conquest of air and space, and to the current state of aerospace


200. General Aeronautics and Astronautics. Prerequisite: Physics l40, preceded or accompanied by Eng. l02. I and II. (2).

Introduction to aerospace engineering. Elementary problems designed to orient the student in the

program of aerospace engineering, together with a discussion of the current state of aerospace

developments and the role of the engineer. Recitations and demonstrations.

300. Elements of Space Science and Technology. Prerequisite: Math. 2l6; Physics 240. (3).Scientific and technological aspects of current space flights, mission goals, the space environment,

vehicle characteristics, performance, and flight paths. Mission support: communications, power,

computers, etc. Open to all University students.

301. Laboratory I. Prerequisite: preceded or accompanied b\ Elec.-Comp. Eng. 3l4. I and II.(2).


principles of electronics, circuit analysis, transducers, modem laboratory instrumentation, experimental methods, and data analysis. Experiments involve simple measurement and instrumentation

problems.

302. Laboratory II. Prerequisite: Aero. Eng. 30l. I and II. (2).Continuation of the material in Aero. Eng. 30l.

314(Mech. Eng. 314). Structural Mechanics I. Prerequisite: Mech. Eng. 2ll. I and II. (3).Review of plane states of stress and strain; basic equations of plane elasticity and selected problems;failure criteria and applications; energy principles of structural theory; thin-walled beam theory.

320. Compressible Flow and Propulsion 1. Prerequisite: Mech. Eng. 235. I and II. (3).First part of an aerodynamics sequence designed to study the fundamental principles and their

applications; physical nature of fluids, conservation laws; nozzles and diffusers; shock waves;


330. Aerodynamics II. Prerequisite: Aero. Eng. 320 or introductory course in fluid mechanics. Iand II. (3).

Second part of an aerodynamics sequence designed to study the fundamental principles and their

applications; viscous effects in laminar and turbulent flows; boundary layer theory; concepts ofinstability and transition to turbulent flow; flows under the influence of gravitational and electromagneticforces.

340. Mechanics of Flight. Prerequisite: Aero. Eng. 200. Mech. Eng. 240. l and II. (3).Mechanics of a particle applied to the analysis of vehicle flight paths. Rigid body mechanics appliedto translational and rotational vehicle motion. Analysis of vehicle motion and static and dynamic

stability using perturbation theory.

350(Math. 350). Aerospace Engineering Analysis. Prerequisite: Math. 2l6. I and II. (3).Formulation and solution of some of the elementary initial- and boundary-value problems relevant to

aerospace engineering. Application of Fourier series, separation of variables, and vector analysis to

problems of forced oscillations, wave motion, diffusion, elasticity, and perfect-fluid theory.

380. Undergraduate Seminar. Prerequisite: junior standing. (l).A series of seminars by noted outside speakers designed to acquaint undergraduates with both current

problems and state of the art of the aerospace industry. Will involve a short term project or paper

pertinent to one of the seminar topics.


Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:1

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

44

5O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

AEROSPACE ENGINEERING I l25

4U(Appl. Mech. 411)(Civ. Eng. 411KNav. Arch. 411). Finite Element Applications. Prerequisite:

Eng. l02, Mech. Eng. 2ll. I. (3).The application of user oriented finite element computer programs for solving practical structuralmechanics problems of frames, 2-D and 3-D solids, plates, shells, etc., and displaying the solutions



414(Appl. Mech. 414). Structural Mechanics II. Prerequisite: Aero. Eng. 3l4. l and II. (3).Introduction to plate theory. Stability of structural elements; columns and beam columns; plate in

compression and shear; secondary instability of columns. Introduction to matrix methods of deformation analysis; structural dynamics.

420. Aerodynamics m. Prerequisite: Aero. Eng. 320. and Aero. Eng. 350 or Math. 450. I andn. (3>.

Third part of an aerodynamic sequence designed to study the fundamental principles and their



423. Aero-Acoustics. Prerequisite: Aero. Eng. 320 or a course in compressible flow. (3).Principles of generation, perception, and abatement of sound generated by fluid flows. Elementaryacoustics; acoustical response of the human ear. Theory and results of measurement of sound



430. Propulsion II. Prerequisite: Aero. Eng. 320. I and II. (3).Performance and analysis of flight-propulsion systems including the reciprocating engine-propeller,turbojet, turboprop, ramjet, and rocket.

433. Combustion Processes. Prerequisite: Aero. Eng. 320. (3).Study of combustion processes with appropriate consideration of the fluid mechanics (aero-thermochemistry); emphasis placed on the physical understanding, applications, performance, pollutionaspects, experimental techniques, and commonality between jet propulsion combustors, internalcombustion engines, and stationary power plants; includes equilibrium constants, chemical kinetics,flames, explosions, liquid drops, particulate formation.


student to certain experimental techniques in the study of actual propulsive devices, using full-scaleor reduced models of the pulsejet. turbojet, ramjet, and rocket motors.








449. Principles of Vertical Take-off and Landing Aircraft. Prerequisite: Aero. Eng. 420. (3).Lifting rotor and propeller analysis in vertical and forward flight; ducted fan analysis; helicopter


452(C.I.C.E. 412) (Elec.-Comp. Eng. 412). Probabilistic Methods in Engineering. Prerequisite:

Elec.-Comp. Eng. 300 or Math. 448. I and II. (3).Basic concepts of probability theory. Random variables: discrete, continuous, and conditional

probability distributions, averages, independence. Introduction to discrete and continuous random

processes: wide sense stationarity, correlation, spectral density. C.I.C.E. students may not receive

graduate credit for both C.I.C.E. 4l2 and C.I.C.E. 5l2.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:1

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

44

5O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


454(C.I.C.E. 482) (Elec.-Comp. Eng. 482). Analog Computation. Prerequisite: Math. 216. (3).Basic theory of analog computers. Analog devices; operational amplifiers, multipliers, function



455(C.I.C.E. 465) (Elec.-Comp. Eng. 465). Computer Graphics Application. Prerequisite:Elec.-Comp. Eng. 270 or l.&O.E. 473 or Comp. <t Comm. Sci. 374 or C.I.C.E. 461. (3).


production of computer animated films. Use of Computek. Tektronix, and PDP graphics terminalsfor electrical circuit design, interactive data smoothing, production of engineering graphs, etc.



464(A.&O.Sci. 464). Upper Atmospheric Science. Prerequisite: senior or graduate standing ina physical science or engineering. I. (3).

An introduction to physical processes in the upper atmosphere; density, temperature, composition,and winds; atmospheric radiation transfer processes and heat balance; the ionosphere; rocket and


471. Automatic Control Systems. Prerequisite: Math. 216. I and II. (3).Transient and steady-state analysis of linear control systems; transfer function and state-space

description of control systems; stability analysis and synthesis methods; application to the design ofautopilots and other modern control systems; introduction to nonlinear control systems and phase

plane analysis.

472(C.I.C.E. 450) (Elec.-Comp. Eng. 450). Fundamentals of Control Systems. Prerequisite:Mech. Eng. 240, Elec.-Comp. Eng. 310. or Elec.-Comp. Eng. 355, and senior standing. I and

II. (3).Concept and importance of control systems. Control system descriptions: state variable and transferfunction representations. System performance and design criteria: stability, sensitivity, time response.Concept of feedback. Time response of linear control systems. Use of Hurwitz, root-locus, Nyquistand Bode methods for analysis and synthesis of linear control systems. Not open to students with


473(C.I.C.E. 451) (Elec.-Comp. Eng. 451). Control Systems Laboratory. Prerequisite: C.I.C.E.450 or Aero. Eng. 471. (2).

Introduction to control system simulation and design. Experiments with physical systems. IIlustrationof basic control principles. Design examples and the use of computer design aids.

481. Airplane Design. Prerequisite: senior standing. I. (4).Power-required and power-available characteristics of aircraft on a comparative basis, calculation ofpreliminary performance, stability, and control characteristics. Design procedure, including layouts

'

and preliminary structural design. Subsonic and supersonic designs. Emphasis on design techniquesand systems approach. Lectures and laboratory.





483. Aerospace System Design. Prerequisite: senior standing. II. (4).Aerospace system design, analysis and integration. Consideration of launch facilities, booster

systems, spacecraft systems, communications, data processing, and project management. Lecturesand laboratory.


510(Appl. Mech. 510)(Mech. Eng. 557). Finite Element Methods in Mechanics I. Prerequisite:Aero. Eng. 4I4(Appl. Mech. 414) or Mech. Eng. 362. I. (3).


Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:1

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

44

5O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


Potential energy. Application to line elements, beams, plane stress, plane strain, and three-dimensional stress. Several computer problems assigned.


(3).Elements of the analysis of structures. Includes plates of various shapes, loading and boundaryconditions, effects of in-plane loading; shells of revolution, cylindrical shells, bending and mem

brane theories; plastic analysis of structures, beams, frames, plates; plastic collapse mechanism.






520. Gasdynamics I. Prerequisite: Aero. Eng. 420 or 425. (3).Gasdynamics at an intermediate level: Thermodynamics; the conservation equations; vorticity theorems;



521. Experimental Gasdynamics. Prerequisite: Aero. Eng. 330 and 420. (3).Experimental methods in modern gasdynamics; physical principles and interpretation. Shop practiceand theory of instrument design: mechanics, electronics, and optics. Measurement of velocity,pressure, density, temperature, composition, energy and mass transfer in fluids and plasmas.

Transducers and laboratory instrumentation in gasdynamic research.


boundary-layer theory; asymptotic concepts; solutions for incompressible boundary layers. Compressible boundary layers; special solutions: transformation of equations; heat transfer in forced and free

convection. Introduction to the mechanics of turbulence: Reynolds stresses: turbulent boundarylayers.

529. Introduction to Energy Transfer. Prerequisite: Aero. Eng. 330. (3).A survey of energy transfer processes including unsteady heat conduction, convection in non-reactive

and reactive flows, and radiation. Aerospace applications, including re-entry heating, ablation,




532. Introduction to Gaskinetics and Real Gas Effects. Prerequisite: Aero. Eng. 420. (3).A study of some modern topics of flow problems not covered in the traditional gasdynamics of ideal

gases: concepts of gaskinetics, aerodynamics of free molecules, shock transition layer, real gas

effects, high temperature effects, multicomponent flows, etc.

535. Rocket Propulsion. Prerequisite: Aero. Eng. 430 or 435. (3).Analysis and performance of liquid and solid propellant rocket powerplants; propellant thermochemistry,heat transfer, system considerations, advanced rocket propulsion techniques.

540( Appl. Mech. 540). Intermediate Dynamics. Prerequisite: Mech. Eng. 240. I. (4).Kinematics of motion, particle dynamics, Lagrange's equations. Rigid body dynamics including

Euler's equations, the Poinsot construction, spin stabilization, the rotation matrix. Vibrations ofcoupled systems, orthogonality relationships, generalized co-ordinates and generalized system pa

rameters.

542. Astrodynamics I. Prerequisite: Aero. Eng. 340. I. (3).The study of motion of spacecraft in a vacuum and in the atmosphere with emphasis on preliminary

mission planning. Analysis of trajectories in suborbital, orbital, lunar, and interplanetary operations.



Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:1

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

44

5O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle







546(Appl. Mech. 547). Advanced Dynamics. Prerequisite: Aero. Eng. 540 or Appl. Mech. 440.

Hamilton's equations, canonical transformations, and Hamilton-Jacobi theory. Applications to orbital





Prerequisite: Mech. Eng. 240. (3).Random mechanical inputs; wind buffeting; earthquakes; surface irregularities. Engineering applications include response of linear spring-mass system and an elastic beam to single and mutiple random






by inertial and other means, including strapped-down and stable-platform inertial systems. Celestial

navigation procedures with deterministic and redundant measurements. Application of Kalman

filtering to recursive navigation theory.

574. Control of Aircraft, Missiles, and Space Vehicles. Prerequisite: preceded or accompanied

by C.I.C.E. 550. II. (2).Analysis and synthesis of autopilots for aircraft and cruise-type missiles. Design of thrust-vector

control systems including effects of elastic structures and fuel sloshing. Attitude control systems for

space vehicles; mechanization using jet thrusters and inertia wheels; gravity gradient moments.

575. Optimization of Space Trajectories. Prerequisite: permission of instructor. II. (3).

Necessary and sufficient conditions for ordinary extremum and variational problems, with emphasison the problem of Bolza. Applications of the calculus of variations to optimal space trajectories.Problems with control and state variable inequality constraints. Iterative computational methods for

two-point boundary-value problems, including the gradient method. Newton's method, and

quasilinearization.

590. Directed Study. (To be arranged).

Individual study of specialized aspects of aerospace engineering. Primarily for graduates.

596. Aurora and Airglow. Prerequisite: permission of instructor. II. (3).Morphology and physics of the aurora and airglow. Emission spectra in the aurora and their atomicand molecular origin; proton aurora; metastable excitation; calculation of emission profiles. Night-and day-glow; pre-dawn and post-twilight enhancements; mid-latitude red arc; excitation mechanisms.


510(Appl. Mech. 510) (Mech. Eng. 557). II. (3).Advanced topics in finite element theory. Plates, shells, large deflections, stability, plasticity,



Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:1

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

44

5O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


620. Dynamics of Viscous Fluids. Prerequisite: Aero. Eng. 520. (3).Navier-Stokes equations; low Reynolds number flows; incompressible and compressible laminarboundary layers; boundary layer stability and transition to turbulence; turbulent boundary layers,wakes, and jets.


transonic flow.


electromagnetic and gravity fields. Invariant analysis of stress-strain relations. Maxwell's equations,analysis of electromagnetic stresses and energy dissipation in moving media, the equations of motionand energy in a moving fluid, and some solutions of the complete equations.

628. Statistical Theory of Fluids. Prerequisite: Aero. Eng. 532. (3).A study of the flows of neutral and charged particles from the viewpoint of kinetic theory;Chapman-Enskog theory of transport phenomena, dynamics of rarefied gases, plasma kineticswithout external magnetic field, plasma oscillations and Landau damping, microinstabilities, plasmainteractions.

632. Gas Flows with Chemical Reactions. Prerequisite: Aero. Eng. 532. 620. (3).Thermodynamics of gas mixtures, chemical kinetics, conservation equations for multicomponentreacting gas mixtures. Deflagration and detonation waves. Nozzle flows and boundary layers withreaction and diffusion.

673<Elec.-Comp. Eng. 673) (Nuc. Eng. 673). Topics in Theoretical Plasma Physics. Prerequisite:Nuc. Eng. 571 or Elec.-Comp. Eng. 580 or Aero. Eng. 726. 1 and II. (3). This course may be

taken for credit more than once.An advanced course in theoretical plasma physics covering topics of current research interest.

Specific content will vary from year to year. Representative topics include: studies of weakly ionized

plasmas with applications to gas lasers; space plasmas; laser fusion plasmas; and nonlinear plasmadynamics and plasma turbulence.



726. Introduction to Plasma Dynamics. Prerequisite: permission of instructor. (3).Physical properties of a plasma; particle orbit theory; collective phenomena in a plasma; kinetic

equations for a plasma; instabilities; transport phenomena and derivation of the magnetohydrodynamic

equations.

729. Special Topics in Gasdynamics. Prerequisite: permission of instructor. (To be arranged).Advanced topics of current interest.







990. Dissertation/Pre-Candidate. I and II (2-8); Ma and Ulb. (1-4).Election for dissertation work by doctoral student not yet admitted to status as a Candidate.


doctoral candidate. I and II (8); IIia and Ulb. (4).Election for dissertation work by doctoral student who has been admitted to status as a Candidate.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:1

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

44

5O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:1

7 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

44

5O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle









100. Introduction to Flight. (2).An introduction to the physical principles of flight within the atmosphere and in space, to the major

historical developments in the conquest of air and space, and to the current state of aerospace


200. General Aeronautics and Astronautics. Prerequisite: Physics 140, preceded or accompanied by Eng. 102. I and U. (2).

Introduction to aerospace engineering. Elementary problems designed to orient the student in the



300. Elements of Space Science and Technology. Prerequisite: Math. 216: Physics 240. (3).Scientific and technological aspects of current space flights, mission goals, the space environment,



301. Laboratory I. Prerequisite: preceded or accompanied by Elec.-Comp. Eng. 314. I and II.(2).


principles of electronics, circuit analysis, transducers, modern laboratory instrumentation, experimental methods, and data analysis. Experiments involve simple measurement and instrumentation

problems.

302. Laboratory II. Prerequisite: Aero. Eng. 301. I and II. (2).Continuation of the material in Aero. Eng. 301.

314(Mech. Eng. 314). Structural Mechanics I. Prerequisite: Mech. Eng. 211. I and II. (3).Review of plane states of stress and strain; basic equations of plane elasticity and selected problems;failure criteria and applications; energy principles of structural theory; thin-walled beam theory.




330. Aerodynamics II. ' Prerequisite: Aero. Eng. 320 or introductory course in fluid mechanics. Iand II. (3).


applications; viscous effects in laminar and turbulent flows; boundary layer theory; concepts ofinstability and transition to turbulent flow; flows under the influence of gravitational and electromagneticforces.

340. Mechanics of Flight. Prerequisite: Aero. Eng. 200, Mech. Eng. 240. I and II. (3).Mechanics of a particle applied to the analysis of vehicle flight paths. Rigid body mechanics appliedto translational and rotational vehicle motion. Analysis of vehicle motion and static and dynamicstability using perturbation theory.

350(Math. 350). Aerospace Engineering Analysis. Prerequisite: Math. 216. I and II. (3).Formulation and solution of some of the elementary initial- and boundary-value problems relevant to

aerospace engineering. Application of Fourier series, separation of variables, and vector analysis toproblems of forced oscillations, wave motion, diffusion, elasticity, and perfect-fluid theory.

380. Undergraduate Seminar. Prerequisite: junior standing. (1).A series of seminars by noted outside speakers designed to acquaint undergraduates with both currentproblems and state of the art of the aerospace industry. Will involve a short term project or paperpertinent to one of the seminar topics.


Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:1

7 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

44

5O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

AEROSPACE ENGINEERING I I27

41 1(Appi. Mech. 41 lKCiv. Eng. 41 lXNav. Arch. 411). Finite Element Applications. Prerequisite:Eng. 102, Mech. Eng. 211. I. (3).

The application of user oriented finite element computer programs for solving practical structuralmechanics problems of frames, 2-D and 3-D solids, plates, shells, etc., and displaying the solutions



414(Appl. Mech. 414). Structural Mechanics II. Prerequisite: Aero. Eng. 314. I and II. (3).Introduction to plate theory. Stability of structural elements; columns and beam columns; plate in

compression and shear; secondary instability of columns. Introduction to matrix methods of deformation analysis; structural dynamics.

416. Theory of Plates and Shells. Prerequisite: Mech. Eng. 21I. Math. 450 or Aero. Eng. 350. (3).

Linear elastic plates, linear theory of membranes. Bending of axisymmetric and non-axisymmetriclinear shells, vibrations of shells, finite element techniques for solving plates and shell problems.

420. Aerodynamics III. Prerequisite: Aero. Eng. 320. and Aero. Eng. 350 or Math. 450; precededor accompanied by Aero. Eng. 330. I and II. (3).

Third part of an aerodynamic sequence designed to study the fundamental principles and their

applications; inviscid flows and fundamentals of Held theory; generation of airfoil lift; thin airfoil


423. Aero-Acoustics. Prerequisite: Aero. Eng. 320 or a course in compressible flow. (3).Principles of generation, perception, and abatement of sound generated by fluid flows. Elementaryacoustics; acoustical response of the human ear. Theory and results of measurement of sound



424. Applied Aerodynamics. Prerequisite: Aero. Eng. 420. (3).Topics related to flow about aircraft wings and bodies and the resulting aerodynamic forces at

subsonic, transonic and supersonic speeds. Potential flows, boundary layers, shock waves, separation,transition, turbulence, effects of Mach and Reynolds numbers. Discussion and explanation of analyticalmethods, numerical methods, and experimental results. Selected other applications.

430. Propulsion II. Prerequisite: Aero. Eng. 320. I and II. (3).Performance and analysis of flight-propulsion systems including the reciprocating engine-propeller,turbojet, turboprop, ramjet, and rocket.

433. Combustion Processes. Prerequisite: Aero. Eng. 320. (3).Study of combustion processes with appropriate consideration of the fluid mechanics (aero-thermochemistry); emphasis placed on the physical understanding, applications, performance, pollution

aspects, experimental techniques, and commonality between jet propulsion combustors, internalcombustion engines, and stationary power plants; includes equilibrium constants, chemical kinetics,flames, explosions, liquid drops, particulate formation.


student to certain experimental techniques in the study of actual propulsive devices, using full-scaleor reduced models of the pulsejet, turbojet, ramjet, and rocket motors.

440. Vehicle Systems Performance. Prerequisite: junior standing. (3).Role of performance in systems analysis: mathematical modeling; identification of constraints,







449. Principles of Vertical Take-off and Landing Aircraft. Prerequisite: Aero. Eng. 420. (3).Lifting rotor and propeller analysis in vertical and forward flight; ducted fan analysis; helicopter

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:1

7 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

44

5O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle



452(C.I.C.E. 412) (Elec.-Comp. Eng. 412). Probabilistic Methods in Engineering. Prerequisite:

Elec.-Comp. Eng. 300 or Math. 448. I and II. (3).Basic concepts of probability theory. Random variables: discrete, continuous, and conditional

probability distributions, averages, independence. Introduction to discrete and continuous random


graduate credit for both C.I.C.E. 4l2 and C.I.C.E. 5l2.

454(C.I.C.E. 482) (Elec.-Comp. Eng. 482). Analog Computation. Prerequisite: Math. 2l6. (3).Basic theory of analog computers. Analog devices; operational amplifiers, multipliers, function



455(C.I.C.E. 465) (Elec.-Comp. Eng. 465). Computer Graphics Application. Prerequisite:

Elec.-Comp. Eng. 270 orl.&O.E. 473 or Comp. & Comm. Sci. 374 or C.l.C.E. 46l. (3).Application of several software packages and display devices for engineering problem solving and

production of computer animated films. Use of Computek, Tektronix, and PDP graphics terminals




464(A.&O.Sci. 464). Upper Atmospheric Science. Prerequisite: senior or graduate standing in

a physical science or engineering. I. (3).An introduction to physical processes in the upper atmosphere; density, temperature, composition,and winds; atmospheric radiation transfer processes and heat balance; the ionosphere; rocket and


471. Automatic Control Systems. Prerequisite: Math. 2l6. I and II. (3).Transient and steady-state analysis of linear control systems; transfer function and state-space

description of control systems; stability analysis and synthesis methods: application to the design ofautopilots and other modem control systems; introduction to nonlinear control systems and phase

plane analysis.

472(C.I.C.E. 450) (Elec.-Comp. Eng. 450). Fundamentals of Control Systems. Prerequisite:Mech. Eng. 240, Elec.-Comp. Eng. 3l0, or Elec-Comp. Eng. 355, and senior standing. I and

II. (3).Concept and importance of control systems. Control system descriptions: state variable and transferfunction representations. System performance and design criteria: stability, sensitivity, time response.

Concept of feedback. Time response of linear control systems. Use of Hurwitz, root-locus, Nyquistand Bode methods for analysis and synthesis of linear control systems. Not open to students withcredit for Aero. Eng. 47l.

473(C.I.C.E. 451) (Elec.-Comp. Eng. 451). Control Systems Laboratory. Prerequisite: C.l.C.E.450 or Aero. Eng. 47l. (2).

Introduction to control system simulation and design. Experiments with physical systems. Illustrationof basic control principles. Design examples and the use of computer design aids.

481. Airplane Design. Prerequisite: senior standing. I. (4).Power-required and power-available characteristics of aircraft on a comparative basis, calculation ofpreliminary performance, stability, and control characteristics. Design procedure, including layoutsand preliminary structural design. Subsonic and supersonic designs. Emphasis on design techniquesand systems approach. Lectures and laboratory.





Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:1

7 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

44

5O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


483. Aerospace System Design. Prerequisite: senior standing. II. (4).

Aerospace system design, analysis and integration. Consideration of launch facilities, booster

systems, spacecraft systems, communications, data processing, and project management. Lectures

and laboratory.


510(Appl. Mech. 510)(Mech. Eng. 557). Finite Element Methods in Mechanics I. Prerequisite:Aero. Eng. 414(Appl. Mech. 414) or Mech. Eng. 362. I. (3).


Potential energy. Application to line elements, beams, plane stress, plane strain, and three-



(3).Elements of the analysis of structures. Includes plates of various shapes, loading and boundaryconditions, effects of in-plane loading; shells of revolution, cylindrical shells, bending and mem

brane theories; plastic analysis of structures, beams, frames, plates; plastic collapse mechanism.






518(Appl. Mech. 518). Theory of Elastic Stability I. Prerequisite: Appt. Mech. 511 . I and II. (3).Elastic and inelastic buckling of bars and frameworks; variational principles and numerical solutions;

lateral buckling of beams. Instability of rings.

520. Gasdynamics I. Prerequisite: Aero. Eng. 420. (3).Gasdynamics at an intermediate level: Thermodynamics; the conservation equations; vorticity theorems;



521. Experimental Gasdynamics. Prerequisite: Aero. Eng. 330 and 420. (3).

Experimental methods in modern gasdynamics; physical principles and interpretation. Shop practiceand theory of instrument design: mechanics, electronics, and optics. Measurement of velocity,

pressure, density, temperature, composition, energy and mass transfer in fluids and plasmas.

Transducers and laboratory instrumentation in gasdynamic research.


boundary-layer theory; asymptotic concepts; solutions for incompressible boundary layers. Compres

sible boundary layers; special solutions; transformation of equations; heat transfer in forced and free

convection. Introduction to the mechanics of turbulence; Reynolds stresses; turbulent boundary

layers.

529. Introduction to Energy Transfer. Prerequisite: Aero. Eng. 330. (3).A survey of energy transfer processes including unsteady heat conduction, convection in non-reactive

and reactive flows, and radiation. Aerospace applications, including re-entry heating, ablation,




532. Introduction to Gaskinetics and Real Gas Effects. Prerequisite: Aero. Eng. 420. (3).

A study of some modern topics of flow problems not covered in the traditional gasdynamics of ideal

gases: concepts of gaskinetics, aerodynamics of free molecules, shock transition layer, real gas

effects, high temperature effects, multicomponent flows, etc.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:1

7 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

44

5O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


535. Rocket Propulsion. Prerequisite: Aero. Eng. 430. (3).Analysis and performance of liquid and solid propellant rocket powerplants; propellant thermochemistry,heat transfer, system considerations, advanced rocket propulsion techniques.

540(Appl. Mech. 540). Intermediate Dynamics. Prerequisite: Mech. Eng. 240. I. (4).Kinematics of motion, particle dynamics, Lagrange's equations. Rigid body dynamics includingEuler's equations, the Poinsot construction, spin stabilization, the rotation matrix. Vibrations ofcoupled systems, orthogonality relationships, generalized co-ordinates and generalized system pa

rameters.

542. Astrodynamics I. Prerequisite: Aero. Eng. 340. I. (3).The study of motion of spacecraft in a vacuum and in the atmosphere with emphasis on preliminarymission planning. Analysis of trajectories in suborbital, orbital, lunar, and interplanetary operations








546(Appl. Mech. 547). Advanced Dynamics. Prerequisite: Aero. Eng. 540 or Appl. Mech. 440.

(3).Hamilton's equations, canonical transformations, and Hamilton-Jacobi theory. Applications to orbital





Prerequisite: Mech. Eng. 240. (3).Random mechanical inputs; wind buffeting; earthquakes; surface irregularities. Engineering applications include response of linear spring-mass system and an elastic beam to single and multiple random



565(Appl. Mech. 565). Optimal Structural Design. Prerequisite: Aero. Eng. 414 and 350. l.(3).Optimal design of structural elements (bars, trusses, frames, plates, sheets) and systems; variational

formulation for discrete and distributed parameter structures; sensitivity analysis; optimal material

distribution and layout; design for criteria of stiffness, strength, buckling, and dynamic response.




by inertial and other means, including strapped-down and stable-platform inertial systems. Celestial

navigation procedures with deterministic and redundant measurements. Application of Kalmanfiltering to recursive navigation theory.

574. Control of Aircraft, Missiles, and Space Vehicles. Prerequisite: preceded or accompaniedby C.I.C.E. 550. II. (2).

Analysis and synthesis of autopilots for aircraft and cruise-type missiles. Design of thrust- vectorcontrol systems including effects of elastic structures and fuel sloshing. Attitude control systems forspace vehicles; mechanization using jet thrusters and inertia wheels; gravity gradient moments.

575. Optimization of Space Trajectories. Prerequisite: permission of instructor. II. (3).Necessary and sufficient conditions for ordinary extremum and variational problems, with emphasison the problem of Bolza. Applications of the calculus of variations to optimal space trajectories.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:1

7 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

44

5O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


Problems with control and state variable inequality constraints. Iterative computational methods for

two-point boundary-value problems, including the gradient method. Newton's method, and

quasilinearization.


5%. Aurora and Airglow. Prerequisite: permission of instructor. II. (3).Morphology and physics of the aurora and airglow. Emission spectra in the aurora and their atomic

and molecular origin; proton aurora; metastable excitation; calculation of emission profiles. Night-and day-glow; pre-dawn and post-twilight enhancements; mid-latitude red arc; excitation mecha

nisms.


5I0(Appl. Mech. 510) (Mech. Eng. 557). II. (3).Advanced topics in finite element theory. Plates, shells, large deflections, stability, plasticity,






transonic flow.


electromagnetic and gravity fields. Invariant analysis of stress-strain relations. Maxwell's equations,

analysis of electromagnetic stresses and energy dissipation in moving media, the equations of motion

and energy in a moving fluid, and some solutions of the complete equations.

628. Statistical Theory of Fluids. Prerequisite: Aero. Eng. 532. (3).A study of the flows of neutral and charged particles from the viewpoint of kinetic theory;Chapman-Enskog theory of transport phenomena, dynamics of rarefied gases, plasma kineticswithout external magnetic field, plasma oscillations and Landau damping, microinstabilities, plasmainteractions.

632. Gas Flows with Chemical Reactions. Prerequisite: Aero. Eng. 532, 620. (3).Thermodynamics of gas mixtures, chemical kinetics, conservation equations for multicomponentreacting gas mixtures. Deflagration and detonation waves. Nozzle flows and boundary layers withreaction and diffusion.

673(Elec.-Comp. Eng. 673) (Nuc. Eng. 673). Topics in Theoretical Plasma Physics. Prerequisite:Nuc. Eng. 571 or Elec.-Comp. Eng. 580 or Aero. Eng. 726. I and II. (3). This course may be

taken for credit more than once.An advanced course in theoretical plasma physics covering topics of current research interest.

Specific content will vary from year to year. Representative topics include: studies of weakly ionizedplasmas with applications to gas lasers; space plasmas; laser fusion plasmas; and nonlinear plasmadynamics and plasma turbulence.




equations for a plasma; instabilities; transport phenomena and derivation of the magnetohydrodynamicequations.


Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:1

7 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

44

5O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle








990. Dissertation Prt-C andidatt. I and II (2-8); IIia and U\b. (l-4).Election for dissertation work by doctoral student not yet admitted to status as a Candidate.


doctoral candidate. I and II (8): IIia and \Ub. (4).Election for dissertation work by doctoral student who has been admitted to status as a Candidate.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:1

7 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

44

5O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

3 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle





158 / COMPUTER, INFORMATION AND CONTROL ENGINEERING

Computer, Information and Control Engineering

Program Office: 1520 East Engineering, phone (313) 764-9387


401(Elec.-Comp. Eng. 401) (Math. 419). Linear Spaces and Matrix Theory. Prerequisite:Math. 216 or 286. I and II. (3).

Finite dimensional linear spaces and matrix representations of linear transformations. Bases, subspaces,determinants, eigenvectors, and canonical forms. Structure of solutions of systems of linear equa

tions. Applications to differential and difference equations. The course provides more depth and

content than Math. 417. Math. 513 is the proper election for students contemplating research in

mathematics. Not open to students with credit for Math 417 or 513.

412(Aero. Eng. 452) (Elec.-Comp. Eng. 412). Probabilistic Methods in Engineering. Prerequisite: Elec.-Comp. Eng. 300 or Math. 448. I and II. (3).

Basic concepts of probability theory. Random variables: discrete, continuous, and conditionalprobability distributions, averages, independence. Introduction to discrete and continuous random


graduate credit for both C.I.C.E. 412 and C.I.C.E. 512.

424(Elec.-Comp. Eng. 424). Signal Transmission for Computers and Communications.Prerequisite: Math. 448 or Math. 300 (Elec.-Comp. Eng. 300). II. (3).

Theory and behavior of elements in communication systems. Transmission of pulses on lines using

Laplace transform analysis; impedance matching: propagation time in computers; noise immunity oflogic elements; pulse deterioration and regeneration; common and difference modes; line construc

tions; distributed circuits; crosstalk; pulse storage and retrieval in computers; superconducting lines:selection of systems components.

430(Elec.-Comp. Eng. 430). Signal Processing and Analysis. Prerequisite: Elec.-Comp. Eng.300 and Elec.-Comp. Eng. 215 or 310. I and II. (4).

Fundamentals of the analysis and processing of continuous and discrete signals. Linear systems and

filtering. Discrete Fourier Transforms (DFT, FFT) and z transforms. Sampling Theorem. Introduction to analog and digital communications. Computer based simulation and data processing are

used to demonstrate the above concepts in a laboratory setting.

432(Elec.-Comp. Eng. 432). Analog Communication Signals and Systems. Prerequisite:Elec.-Comp. Eng. 430. I and II. (3).

Mathematical analysis of the signals and signal processing used in analog communication systems;

spectral analysis, signal transmission; amplitude, phase, frequency and pulse modulation; modulationand demodulation techniques; frequency and time multiplexing; analysis of signal to noise ratio;

application to radio and television.

434(Elec.-Comp. Eng. 434). Digital Communication Signals and Systems. Prerequisite: Elec.-Comp. Eng. 430, and Stat. 412 or C.I.C.E. 412. I. (3).

Digital transmission techniques in data communications, with application to computer and spacecommunications; design and detection of digital signals for low error rate; forward and feedback

transmission techniques; matched filters, modems, block and convolutional coding, Viterbi decoding.

436(Elec.-Comp. Eng. 436). Digital Signal Processing. Prerequisite: Elec.-Comp. Eng. 430.

n. <3).

Analysis techniques used in computer processing of signals. Analog to digital conversion. Recursiveand nonrecursive digital filtering, correlation and matched filtering. Time series analysis of waveforms,z transforms, fast Fourier transforms, complex demodulation, data compression, cepstrum techniques,and spectral estimation.

450(Aero. Eng. 472) (Elec.-Comp. Eng. 450). Fundamentals of Control Systems. Prerequisite:Mech.Eng. 240, Elec.-Comp. Eng. 310, or Elec.-Comp. Eng. 355, and senior standing. Iand II. (3).

Concept and importance of control systems. Control system descriptions: state variable and transfer

function representations. System performance and design criteria: stability, sensitivity, time response.

Concept of feedback. Time response of linear control systems. Use of Hurwitz, root-locus, Nyquist

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

3 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

COMPUTER, INFORMATION AND CONTROL ENGINEERING I 159

and Bode methods for analysis and synthesis of linear control systems. Not open to students with


451(Elec.-Comp. Eng. 451) (Aero. Eng. 473). Control Systems Laboratory. Prerequisite:'Cl.C.E. 450 or Aero. Eng. 471. (2).

Introduction to control system simulation and design. Experiments with physical systems. Illustrationof basic control principles. Design examples and use of computer design aids.

460. Structure of Digital Computers. Prerequisite: graduate standing. I and II. (4).

An introduction to the important hardware concepts of digital computation: logical design, machine

organization, machine language, assembly language. Students write computer programs in machine

and/or assembly languages. Laboratory. Not open to students with credit for Elec-Comp. Eng. 365.

464(Elec.-Comp. Eng. 464). Cellular Computers and Image Processing. Prerequisite: Elec-Comp. Eng. 367; and Elec-Comp. Eng. 365 or C.I.C.E. 460; and senior standing. (3).

Study of computers consisting of large numbers of identical programmable electronic cells as highlyparallel digital image processors. Digital image transformations implemented as programmable

sequences of parallel nearest neighbor operations. Automatic extraction of pictorially encoded

information. Topics include image algebra, cytocomputers, biomedical applications, and robotics.

465(Aero. Eng. 455) (Elec.-Comp. Eng. 465). Computer Graphics Application. Prerequisite:Elec-Comp. Eng. 270 or l.&O.E. 473 or Comp. & Comm. Sci. 374. (3).


production of computer animated films. Use of Computek, Tektronix, and PDP graphics terminals


POLYGRAPHICS and BEFLIX computer animation packages and their use in MTS. Production oftwo or three films using graphics terminals.

466(Elec.-Comp. Eng. 466). Digital Design Laboratory. Prerequisite: Elec.-Comp. Eng. 366

or Cl.C.E. 460. I and II. (2%

Realistic design problems in digital systems engineering. Design, construction, and demonstration ofdevices which operate alone or in conjunction with digital computers in the laboratory. Lecture and

laboratory.

467(Elec.-Comp. Eng. 467). Switching and Sequential Systems. Prerequisite: Elec.-Comp.Eng. 367 and senior standing, or graduate standing. I and II. (3).

An introduction to the theory of switching networks and sequential systems. Switching functions and

realizations, threshold logic, fault detection, connectedness and distinguishability, equivalence and

minimality, state identification-, system decomposition.

468( Elec.-Comp. Eng. 468). Theory of Languages and Computation. Prerequisite: Elec.-Comp. Eng. 36T; Elec-Comp. Eng. 270 or l.&O.E. 473 or Comp. & Comm. Sci. 374;

and senior standing. I. (3).An introduction to the study of computer behavior through formal models of languages and

. computation. Formal grammars and languages; effective procedures; algorithms; formal models ofprocedures and algorithms, e.g. Turing machines, Wang programs; connections between languages

and machines that accept them; complexity of computation.

469(Elec.-Comp. Eng. 469). Application of Real Time Computer Systems. Prerequisite: Elec.-Comp. Eng. 270 or 272; and 300. I and II. (4).

Principles of application of real time computer systems to engineering problems. Topics include:

computer characteristics needed for real time use, mini/micro computer operating systems, man-

computer communication, basic digital logic design, analog signal processing and conversion, and

inter-computer communication. Topics investigated via laboratory using microprocessor system.

Three lectures and one three hourjaboratory per week.

478(Elec.-Comp. Eng. 478) (l.&O.E. 478). Interactive Computer Graphics. Prerequisite:Elec.-Comp. Eng. 364 or l.&O.E. 373. and senior standing. I and II. (3).

Graphics devices and fundamentals of operation. Two dimensional and three dimensional

transformations. Interactive graphical techniques and applications. Three dimensional graphics,

perspective transformation, hidden line elimination. Data structures and languages for graphics.

Interactive graphical programming.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

3 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


479(Elec.-Comp. Eng. 479) (Comp. & Comm. Sci. 478). Software Engineering. Prerequisite:Elec.-Comp. Eng. 364. or preceded or accompanied by Comp. & Comm. Sci. 476: andsenior standing. (4).

Pragmatic aspects of the production of software systems, dealing with structuring principles,design methodologies and informal analysis. Emphasis is given to development of large, complexsoftware systems. A term project is usually required.

482(Aero. Eng. 454) (Elec.-Comp. Eng. 482). Analog Computation. Prerequisite: Math. 216.

(3).Basic theory of analog computers. Analog devices: operational amplifiers, multipliers, functiongenerators. Analog simulation of linear and nonlinear dynamic systems, including ordinary and


494(Elec.-Comp. Eng. 494) (I.&O.E. 494) (Mech. Eng. 484). Robot Applications. Prerequisite:(Elec.-Comp. Eng. 270 or Elec.-Comp. Eng. 365 or l.&O.E. 373 or Mech. Eng. 340) and

(Mech. Eng. 240 or Elec.-Comp. Eng. 355) and senior standing. Not open to students with

previous credit for C.I .C .E . 509. II. (3).Basic concepts in the organization and operation of microcomputer-controlled manipulators. Ex

periments include kinematics, manipulation, dynamics, trajectory planning and programming

language for robots. Applications of computer-controlled robots in manufacturing and programmable

automation.

500. Linear Dynamical Systems. Prerequisite: C.I.C.E. 401, or Math. 404 and Math. 417; andElec.-Comp. Eng. 300 or Math. 448. I and II. (3). '

Models of dynamical systems and their linear specializations: difference and differential equations,

general axiomatic formulations. Rigorous treatment of numerous system concepts: linearity, time

invariance, causality, input-output representations, controllability, observability, equivalence, ca

nonical decomposition, minimal realizations, inverse systems, stability.

501. Function Space Methods in System Theory. Prerequisite: CJ.C.E. 401. (3).Introduction to the description and analysis of systems using function analytic methods. Metric

spaces, normed linear spaces, Hitbert spaces, resolution spaces. Emphasis on using these concepts in

systems problems.

503(Elec.-Comp. Eng. 503) (I.&O.E. 503). Social Decision Making. Prerequisite: Stat. 310 orI. &O.E. 315 or C.I.C.E. 412 or C.I.C.E. 512. (3).

Elementary decision analysis, examples in public sector; basic problems in social decision making.Social values and preferences, multiattribute utility functions, subjectivity measurement. Pareto

optimality, Arrow's impossibility theorem. Group decision analysis, two-person game theory. Socialdecision processes, strategy of conflicts.

505. Simulation Methods for Large Scale Systems. Prerequisite: C.I.C.E. 412 or C J.C.E. 512:

(3).

Modeling and digital computer simulation of large scale systems. Discrete event simulation, statistical

tests, random number generators, experimental design of simulation experiments. Introduction tosimulation languages. The course usually involves a project.

507. Artificial Intelligence. Prerequisite: Elec.-Comp. Eng. 364 or Comp. & Comm. Sci. 476.and senior standing. (3).

Representation of information; search methods and the use of heuristic information; automatic

theorem proving; analysis of question-answering systems; robot problem solving systems; visionsystems; game playing programs; languages for artificial intelligence.

509. Introduction to Robotics: Theory and Practice. Prerequisite: Elec.-Comp. Eng. 364. (3).Methods of design and operation of computer-based robots. Kinematics and dynamics of a six-

jointed arm; force, moment, torque, compliance, control methods, trajectory planning. Integrationof computer vision systems to form hand-eye coordinated systems. Man-machine communication

via high-level language.

512. Probability and Random Processes. Prerequisite: C.I.C.E. 412 or graduate standing. 1 andII. (4).

Rigorous study of the basic concepts of probability theory: sample spaces, probability axioms,random variables, probability distribution functions, statistical averages. Introduction to random

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

3 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

COMPUTER, INFORMATION AND CONTROL ENGINEERING I 161

processes: stationarity, covariance and correlation functions, Poisson processes, Gaussian processes.

Recitation. C.I.C.E. students may not .receive graduate credit for both C.I.C.E. 412 and C.l.C.E.512. . *515. Continuous State Stochastic Processes. Prerequisite: C.I.C.E. 512. II. (3).Gaussian processes. Correlation functions. Stationary processes; ergodic properties and spectral

theory. Response of linear systems to stochastic inputs. Introduction to spectral estimation. Least

mean square error linear filtering, estimation and prediction. Recursive filtering. Examples and

applications in control and communications.

516<Stat. 526) (Math. 526). Discrete State Stochastic Processes. Prerequisite: C.I.C.E. 512

or Math. 525 or Stat. 510. (3).Review of discrete distributions, generating functions, compound distributions, renewal theorem,

systems as Markov chains. Properties of Markov chains: Chapman-Kolmogorov equations, return

and first passage times, classification of states and periodicity, absorption probabilities, forward

equation, stationary distributions, backward equation, ergodicity, limit properties. Branching and

queueing processes: examples from engineering, biological, and social sciences; continudus time

Markov chains, embedded chains, the M/G/l queue, Markovian decision processes, inventory

problems.

521. Signal Detection. Prerequisite: C.I.C.E. 512. (3).Binary decisions and reduction of uncertainty through observation. Likelihood ratios and detection

criteria. Study of signal plus Gaussian noise. Optimum detectors. Interrelation of detection, parame

ter estimation, and noise environment analysis. Application to communications.

522. Analog Communication Theory. Prerequisite: C.I.C.E. 432 and C.I.C.E. 512. I. (3).Statistical methods in the analysis of analog transmission systems; bandwidth, signal-to-noise ratio

and threshold behavior of amplitude, frequency and pulse modulations; phase-locked loops forcoherent detection and FM demodulation; source coding for analog signals, including quantization

and PCM.

524. Digital Communication Theory. Prerequisite: C.I.C.E. 512. D. (3).Fundamentals of design and analysis of digital communication systems for discrete sources; decision

theory and signal space concepts used to derive the optimum coherent and noncoherent receiver in

presence of additive white Gaussian noise; extensions to bandpass and filtered channels; synchronization;

analysis of coded digital communications; Shannon's capacity theory; block and convolutional codes.

530. Information Theory. Prerequisite: C.I.C.E. 512. I. (3).The concepts of source, channel, rate of transmission of information. Entropy and mutual information. The noiseless coding theorem. Noisy channels; the coding theorem for finite state zero memory

channels. Channel capacity. Error bounds. Parity check codes. Source encoding.

536. Image Processing. Prerequisite: C.I.C.E. 512. II. (3).Theory and application of digital image processing. Multi-dimensional signal processing. Random

field models of images. Sampling and quantization. Image compression, enhancement, and restoration.

Segmentation, shape description, and pattern recognition. Reconstruction of pictures from their

projections. Applications to robotics, optics, time-varying imagery, and biomedical images.

540. Optimal Control. Prerequisite: C.I.C.E. 401, or Math. 404 and Math. 417. (3).

Formulation of optimal control problems. Constrained minimization problems in finite dimensional

space; necessary conditions for optimality and their application to discrete-time optical control

problems. Dynamic programming, Hamiiton-Jacobi theory, the Pontryagin necessary conditions.

Applications to time and fuel optimal systems and the linear-quadratic problem. Examples taken from

a variety of fields. Introduction to computational considerations.

542. Applied Optimal Estimation. Prerequisite: C.I.C.E. 401, 412. 450. II. (3).Formulation of optimal estimation problems. Least squares, and generalized least squares techniques.

Recursive techniques and Kalman filtering for linear discrete time systems. Extensions to continuous

time systems, steady state filtering, nonlinear filtering, numerical difficulties, prediction, and

smoothing. Parameter and state identification techniques. The linear-quadratic-gaussian optimal

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

3 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

162 / COMPUTER, INFORMATION AND CONTRdL ENGINEERING

545(1. &O.E. 511) (Math. 562). Continuous Optimization Methods. Prerequisite: Math. 417 (h

Math. 419. I and II. (3).

Survey of continuous optimization problems. Unconstrained optimization problems: unidirectional

search techniques; gradient, conjugate direction, quasi-Newton methods. Introduction to constrained

optimization using techniques of unconstrained optimization through penalty transformations, augmented

Lagrangians, and others. Discussion of computer programs for various algorithms.

550. Nonlinear Control Systems.'

Prerequisite: C.I.C.E. 401, or Math. 404 and Math. 417: and

C.I.C.E. 450 or Aero. Eng. 471. I and II. (3).Modeling of nonlinear control systems by state and operator descriptions. Nonlinear phenomena:

limit cycles, sliding solutions, subharmonics, jump phenomena, domain of stability. Use of phase

plane techniques, describing functions, Liapunov theory and frequency response methods (circle and

Popov criteria) for analyzing and designing nonlinear control systems.

552. Sampled Data Control Systems. Prerequisite: C.I.C.E. 401, or Math. 404 and Math. 417:

and C.I.C.E. 450 or Aero. Eng. 471. II. (3).

Technological reasons for sampling. Sampling, extrapolation, and interpolation processes; quantizing

effects. The z-transform and its application to mixed data systems; steady state and transient

response; stability determination. Compensator design; realization by digital computers..State space

methods for analysis and design.

560 (Elec.-Comp. Eng. 560). VLSI Design. Prerequisite: Elec.-Comp. Eng. 462 and C.I.C.E.565, or Elec.-Comp. Eng. 486 and Elec.-Comp. Eng. 365. II. (4).

Design techniques for rapid implementation of very large scale integrated (VLSI) circuits. MOS

technology and logic. Structured design. Design rules, layout procedures. Design aids: layout,

design rule checking, logic and circuit simulation. Timing. Testability. Architectures for VLSI.Includes group projects to develop, lay out circuits, and produce pattern generator tapes for

subsequent fabrication.

564(Contp. & Comm. Sci. 564). Computing System Evaluation. Prerequisite: Elec.-Comp.Eng. 270 or Comp. & Comm. Sci. 274, and Elec.-Comp. Eng. 365 and C.I.C.E. 512. II. (3).

Theory and application of analytical methods for evaluating the performance and reliability of

computing systems. Measures of performance, reliability, and performability. Reliability evaluation,

classification and representation of faults, stochastic process models, coherent systems. Performance

evaluation: Markovian queuing models, networks of queues. Unified performance —reliability

evaluation.

565. Logical Design of Digital Computers. Prerequisite: C.I.C.E. 460 or Elec.-Comp. Eng.

365. and C.I.C.E. 467. I and II. (3).Advanced course in logical design. Logical properties of devices. Architectural properties, formal

descriptions, and register-transfer simulations of digital systems. Control strategies, including microprogramming. Hardware technology and its relationship to computer structures. Design automation of

digital systems.

567. Automata Theory. Prerequisite: C.I.C.E. 467. (3).A broad, thorough treatment of the structure and behavior of automata with an emphasis on models ofdiscrete-time, time-invariant systems, and general models of computation. Machine simulation and

realization, canonical realizations of sequential behavior, finite-state languages and regular expressions, decomposition of sequential machines. Turing machines and computable functions, partialrecursive functions, and reliable automata.

568. Reliable Computing Systems. Prerequisite: C.I.C.E. 467 or Comp. Comm. Sci. 510 and

Elec.-Comp. Eng. 270 or Comp. & Comm. Sci. 374. II. (3).An introduction to models and methods used in the analysis and design of reliable hardware systems,software systems and computing systems. Aspects of reliability considered include fault-tolerance,

fault detection and diagnosis, reconfiguration, design verification and testing, and reliability evalua

tion.

569. Digital Computer Arithmetic. Prerequisite: C.I.C.E. 460 or Elec.-Comp. Eng. 365, andC.I.C.E. 467. I. (3).

Classification and structure of finite number systems and arithmetic including weighted, redundant,

and signed-digit classes of number systems. Theory of modern high-speed computer arithmetic

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

3 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

COMPUTER. INFORMATION AND CONTROL ENGINEERING I 163

including fast carry logic multiplier recoding, and SRT division. Case studies of general and special

purpose arithmetic processors.

573<Comp. & Comm. Sci. 573). Computer Operating Systems. Prerequisite: Comp. & Comm.

Sci. 476 or Comp. & Comm. Sci. 572 or Elec.-Comp. Eng. 364; and Comp. & Comm. Sci. 382

or Elec.-Comp. Eng. 271 or equivalent assembly language experience. I and II. (4).

Reviews history of computer hardware and related operating system developments. Considers

various operating system functions and their implementations: linking and loading; resource alloca

tion; virtual memory; scheduling; multi-tasking and synchronization; etc. Students write two or three

substantial programs in operating system area.

575(Comp. & Comm. Sci. 575). Compiler Construction. Prerequisite: Comp. & Comm. Sci.476 or Elec.-Comp. Eng. 364. I and II. (4).

Introduction to compiling techniques including parsing algorithms, semantic processing, and

optimization. With the aid of a compiler writing system, the student implements a compiler for a

substantial programming language.

576. Raster Graphics —Principles and Applications. Prerequisite: C.I.C.E. 465 or C.I.C.E.478. I. (3).

A detailed account of modem raster-based computer graphics. Topics include solid area scan

conversion, color theory and application, hidden surface elimination, shading, highlights, animation,

painting, and standardized graphics software.

577(I.&O.E. 577) (C.I.S. 577). Data Management Systems. Prerequisite: Elec.-Comp. Eng.364; or Comp. & Comm. Sci. 476; or l.&O.E. 473: or S.&M.S.IC.I.S. 411 and CI S. 500.

I and II. (3).

Concepts and methods in the definition and management of large integrated data bases for

organizational information systems. Functions and objectives of existing file and data management

systems will be considered and methods of analyzing proposals for new data management software

will be studied. Additional topics will include data base administration, data base design, and

data security problems.

578U.&O.E. 578). Geometric Modeling. Prerequisite: l.&O.E. 478 or C.I.C.E. 465. (3).

Individual or group study of topics in geometric modeling and computer graphics. Geometric

data structures for curves, surfaces, and volume parametization, and topological data structures forvertices, edges, faces, and bodies will be covered. Algorithms for set operations, Euler operations

and deformation will be studied. Design and experimentation with geometric modeling facilities.

580. Hybrid Computation. Prerequisite: C.I.C.E. 482; and Elec.-Comp. Eng. 270 or Comp.& Comm. Sci. 374. (3).

Description of combined analog-digital computer systems. Dynamic error analysis of analog, digital,and hybrid computing systems Dsing operational methods, including the z- transform. Application ofhybrid computers to a variety of engineering problems such as parameter optimization and partialdifferential equations. Lecture and laboratory, including an individually selected laboratory project.

610. Theory of Stochastic Processes. Prerequisite: C.I.C.E. 515. (3).

Measure theoretic treatment of stochastic processes. Analysis and representation of various stochastic

processes using function analytic concepts. Wiener processes, martingales, diffusion processes.

Stochastic integrals, introduction to stochastic differential equations and stochastic calculus.

612. Estimation Theory. Prerequisite: C.I.C.E. 515. (3).

Representations of stochastic processes for statistical estimation. Least squares and linear unbiased

minimum variance estimators. Bayes, min-max, maximum likelihood a posteriori, and maximum

likelihood estimators. Recursive filtering, prediction, and interpolation. Applications to control and

communications.

621. Communication Theory and Design. Prerequisite: C.I.C.E. 522. (3).

Advanced topics in detection, estimation, and modulation theory. Nonlinear modulation theory.

Synchronization systems. Multipath and fading channels. Signal processing in radar and sonar

systems. Voice communication.

625. Channel Coding Theory. Prerequisite: C.I.C.E. 512 and C.I.C.E. 401. II. (3).The theory of channel coding for reliable communication and computer memories. Error correcting

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

3 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


codes; linear, cyclic, and convolutional codes; encoding and decoding algorithms; performance

evaluation of codes on a variety of channels.

626. Source Coding Theory. Prerequisite: C.I.C.E. 512. (3).

Introduction to a variety of source coding techniques such as quantization; block quantization;

and differential, predictive, transform, and tree coding. Introduction to rate-distortion theory

Applications include speech and image coding.

640. Theory of Optimal Control. Prerequisite: CT.C.E. 540 or Aero. Eng. 575. (3).General theoretical questions in optimal control: existence of optimal controls, derivation of neces

sary and sufficient conditions for optimality. Selected special topics: singular control, state con

straints, min-max criteria, systems described by partial differential equations, the second variation

Examples and applications of the theory.

645. Computational Methods in Optimal Control. Prerequisite: C.I.C.E. S45 and either

C.I.C.E. 540 or Aero. Eng. 575. (3).

Development of algorithms for solving optimal control problems. Direct and indirect methods.

Control and state constraints. Penalty functions. Problems with special structure. Computer consider

ations.

665. Systems Design of Digital Computers. Prerequisite: C.I.C.E. 573 and C.I.C.E. 565. (3).

General consideration of computer architecture with attention being given to both the hardware and

the software. Memory hierarchies, look ahead, multi processing, and time sharing.

675(Comp. & Comm. Sci. 675). Compiler Construction Laboratory. Prerequisite: C.I.C.E.(Comp. & Comm. Sci.) 575. (3).

As a group, students design and implement a full compiler. Emphasis is upon the generalization and

innovative use of the basic techniques encountered in the prerequisite course. Possible project topics

are: an optimizing compiler; a compiler for a subset of Pascal: a cross-compiler for a mini- or

micro-computer.

677. Database Design. Prerequisite: C.I.C.E. 577(1. &O.E.IC.I.S. 577). I and II. (3).

Design of logical and physical database structures, implementation of database applications, and

performance evaluation. Requirements analysis techniques, conceptual schema design, tradeoff

analysis for DBMS-specific schemas, access methods, and clustering. Distributed data allocation

and query optimization. Students design and implement a medium-scale database application.Research paper is required.

679(Comp. & Comm. Sci. 678). Formal Aspects of Software Engineering. Prerequisite:C.I C.E. 468 or Comp. & Comm. Sci. 400; and C.I.C.E. 479 or 573 or 575. (3).

Formal approaches to construction of reliable software and design of large-scale software systems.

Topics include the denotational and algebraic approaches to semantics of computation; abstract

data types and specification techniques; formal notions of implementation: synchronization; programverification and logics of programs. Students are required to complete a term project.

699. Directed Individual Study. Prerequisite: permission of instructor. (To be arranged).

701. Special Topics in System Theory. Prerequisite: permission of instructor. (To be arranged).

720. Special Topics in Communication and Information Theory. Prerequisite: permission of

instructor. (To be arranged).

740. Special Topics in Control Theory. Prerequisite: permission of instructor. (To be arranged).

760. Special Topics in Computer Systems. Prerequisite: permission of instructor. (To be arranged).

801. Seminar in System Theory. Prerequisite: permission of instructor. (To be arranged).

820. Seminar in Communication and Information Theory. Prerequisite: permission of instructor. (To be arranged).

840. Seminar in Control Theory. Prerequisite: permission of instructor. (To be arranged).

860. Seminar in Computer Systems. Prerequisite: permission of instructor. (To be arranged)

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

3 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

ECONOMICS I 165

990. Dissertation/Pre-Candidate. I, II, and III. (2-8); IIia and IIk. (1-4).Election for dissertation work by doctoral student not yet admitted to status as Candidate.


doctoral Candidate. I. II, and IH. (8); IIia and IIk. (4).

Election for dissertation work by doctoral student who has been admitted to status as a Candidate.

Economics*

Department Office: 9th floor, Old St. Joseph's Hospital, 300 N. Ingalls, phone (313) 764-2355

Professor Gramlicb, Chairman; Professor Porter, Associate Chairman; Professors Ackley, Anderson,Barlow, Bergstrom, Bornstein, Brazer, Cross, Deardorff, Demberger, Feldstein, Fusfeld, Haber,

Howrey, Holbrook, Hymans, Johnson. Juster, Kmenta, Levinson, Morgan, Mueller, Palmer,

Porter, Rubinfeld, Saxonhouse, Shapiro, Shepherd, Stafford, Steiner, Stem, Stolper, Teigen,Varian, Weisskopf; Associate Professors Adams, Courant. Laitner, Simon; Assistant Professors

Blume, Freedman, Ranney, Webb, Whatley; Lecturers Crafton. and Putallaz.

A. Introductory Courses

Students who earned credit for Economics 201 or 400 prior to Fall Term 1982 are permitted

to enter all those upper-level courses whose prerequisites are designated Economics 201 and 202.

Students who elect Economics 201 in Fall Term 1982 and thereafter will be required to take its

sequel. Economics 202, in order to take any advanced courses in the Economics Department.

201. Principles of Economics I. Prerequisite: Open to second-term freshmen. No credit granted

to those who have completed 400. I, II, IIia, and IIk. (4).The basic ideas of microeconomics: production, consumption, and the markets for outputs and

inputs. The virtues of competitive markets are exposed, and the causes and remedies of such

market failures as monopoly, indivisibility, spillover costs and inequity are examined.

202. Principles of Economics Hi Prerequisite: Econ. 201. No credit granted to those who

have completed Econ. 400. I, II, \Ua, and IIk. (4).

The basic ideas of macroeconomics: employment, inflation, output, and growth. The determinants

of the state of the market economy are explored, and the influence of monetary, fiscal, and other

public policies are examined.

400. Modern Economic Society. Prerequisite: For upperclass and graduate students without

prior credit for principles of economics. I, II, IIia and IIk. (4).A single-term accelerated treatment of the material of Econ. 201 and 202. (Econ. 400 is some

times permitted to serve as a prerequisite for advanced courses in Economics. Students who have

received credit for Econ. 201 and/or 202 may not receive credit for Econ. 400.)

B. Economic Theory and Statistics

401. Intermediate Microeconomic Theory. Prerequisite: Econ. 201 and 202. Math. 112 or 115.

I, n, and IIk. (3).A systematic study of the role of the price system in organizing economic activity and an evaluation

of its effectiveness. Analytical tools are developed and applied to the activities of the household, the

firm, and to their interactions in the market under varying degrees of competition. MICRO

402. Intermediate Macrocconomic Theory. Prerequisite: Econ. 201 and 202, Math. 112 or 115.

I. □. and IIk. (3).A systematic study of the theory of aggregate demand, the degree of utilization of productive

capacity, and the general level of prices. MACRO

' College of Literature. Science, and the Aits

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

3 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle









100. Introduction to Flight. (2).An introduction to the physical principles of flight within the atmosphere and in space, to the

major historical developments in the conquest of air and space, and to the current state ofaerospace developments and their role in national and world affairs.

200. General Aeronautics and Astronautics. Prerequisite: Physics 140. preceded or accompa

nied by Eng. 103. I and II. (2).Introduction to aerospace engineering. Elementary problems designed to orient the student in the



300. Elements of Space Science and Technology. Prerequisite: Math. 216; Physics 240. (3).Scientific and technological aspects of current space flights, mission goals, the space environment,

vehicle characteristics, performance, and flight paths. Mission support: communications, power,computers, etc. Open to all University students.

301. Laboratory I. Prerequisite: preceded or accompanied by Elec.-Comp. Eng. 314. I and

n. (2>.


principles of electronics, circuit analysis, transducers, modem laboratory instrumentation,

experimental methods, and data analysis. Experiments involve simple measurement and instru

mentation problems.

302. Laboratory II. Prerequisite: Aero. Eng. 301. I and II. (2).Continuation of the material in Aero. Eng. 301.

314. Structural Mechanics I. Prerequisite: Mech. Eng. 211 . I and II. (3).Review of plane states of stress and strain; basic equations of plane elasticity and selected

problems; failure criteria and applications; energy principles of structural theory; thin-walledbeam theory.




330. Aerodynamics II. Prerequisite: Aero. Eng. 320 or introductory course in fluid mechanics.

I and H. (3).


applications; viscous effects in laminar and turbulent flows; boundary layer theory; concepts ofinstability and transition to turbulent flow; flows under the influence of gravitational and

electromagnetic forces.

340. Mechanics of Flight. Prerequisite: Aero. Eng. 200, Mech. Eng. 240. I and II. (3).

Mechanics of a particle applied to the analysis of vehicle flight paths. Rigid body mechanics

applied to translational and rotational vehicle motion. Analysis of vehicle motion and static and

dynamic stability using perturbation theory.

350<Math. 350). Aerospace Engineering Analysis. Prerequisite: Math. 216. I and II. (3).

Formulation and solution of some of the elementary initial- and boundary-value problems

relevant to aerospace engineering. Application of Fourier series, separation of variables, and

vector analysis to problems of forced oscillations, wave motion, diffusion, elasticity, and

perfect-fluid theory.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


380. Undergraduate Seminar. Prerequisite: junior standing. (1).A series of seminars by noted outside speakers designed to acquaint undergraduates with both

current problems and state of the art of the aerospace industry. Will involve a short term project or

paper pertinent to one of the seminar topics.


411(Appl. Mech. 411)(Civ. Eng. 411)(Nav. Arch. 411). Finite Element Applications. Prerequisite: Eng. 103, Mech. Eng. 211. I. (3).

The application of user oriented finite element computer programs for solving practical structural

mechanics problems of frames, 2-D and 3-D solids, plates, shells, etc., and displaying the

solutions graphically. Students learn to prepare input data and interpret results. A short

introduction to the underlying theory is also presented.

414(Appl. Mech. 414). Structural Mechanics II. Prerequisite: Aero. Eng. 314. 1 and II. (3).Introduction to plate theory. Stability of structural elements; columns and beam columns; plate in

compression and shear; secondary instability of columns. Introduction to matrix methods ofdeformation analysis; structural dynamics.

416. Theory of Plates and Shells. Prerequisite: Mech. Eng. 211. Math. 450 or Aero. Eng.

350. (3).Linear elastic plates, linear theory of membranes. Bending of axisymmetric and non-axisymmetric

linear shells, vibrations of shells, finite element techniques for solving plates and shell problems.

420. Aerodynamics III. Prerequisite: Aero. Eng. 320, and Aero. Eng. 350 or Math. 450;

preceded or accompanied by Aero. Eng. 330. I and II. (3).Third part of an aerodynamic sequence designed to study the fundamental principles and then-



423. Aero-Acoustics. Prerequisite: Aero. Eng. 320 or a course in compressible flow. (3).Principles of generation, perception, and abatement of sound generated by fluid flows. Elemen

tary acoustics; acoustical response of the human ear. Theory and results of measurement of sound

generated by explosions, sonic booms, jets, boundary layers, and flow excited structural

vibrations. Qualitative assessment of techniques and effectiveness of noise abatement procedures.

424. Applied Aerodynamics. Prerequisite: Aero. Eng. 420. (3).

Topics related to flow about aircraft wings and bodies and the resulting aerodynamic forces at

subsonic, transonic and supersonic speeds. Potential flows, boundary layers, shock waves,

separation, transition, turbulence, effects of Mach and Reynolds numbers. Discussion and

explanation of analytical methods, numerical methods, and experimental results. Selected other

applications.

430. Propulsion II. Prerequisite: Aero. Eng. 320. I and H. (3).Performance and analysis of flight-propulsion systems including the reciprocating engine-

propeller, turbojet, turboprop, ramjet, and rocket.

439. Aircraft Propulsion Laboratory. Prerequisite: Aero. Eng. 320. (2).Series of experiments designed to illustrate the general principles of propulsion and to introduce

the student to certain experimental techniques in the study of actual propulsive devices, using

full-scale or reduced models of the pulsejet, turbojet, ramjet, and rocket motors.


performance parameters, and performance indices. The aircraft performance problem: flight

envelope, aerodynamic approximations, available propulsion systems; takeoff, landing, climb,and range performance. Modem performance optimization techniques. Applications to automobile,

high-speed train, and space vehicle performance analysis.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


447. Flight Testing. Prerequisite: Aero. Eng. 340. (2).

Theory and practice of obtaining flight-test data on performance and stability of airplanes from

actual flight tests. No laboratory fee will be charged, but a deposit covering student insurance and

operating expense of the airplane will be required.

452(C.I.C.E. 412) (Elec.-Comp. Eng. 412). Probabilistic Methods in Engineering.Prerequisite: Elec.-Comp. Eng. 300 or Math. 448. I and II. (3).

Basic concepts of probability theory. Random variables: discrete, continuous, and conditional

probability distributions, averages, independence. Introduction to discrete and continuous ran

dom processes: wide sense stationarity, correlation, spectral density. C.I.C.E. students may not

receive graduate credit for both C.I.C.E. 412 and C.I.C.E. 512.

454<C.I.C.E. 482) (Elec.-Comp. Eng. 482). Analog Computation. Prerequisite: Math. 216.

(3).Basic theory of analog computers. Analog devices; operational amplifiers, multipliers, function



455(C.I.C.E. 465) (Elec.-Comp. Eng. 465). Computer Graphics Application. Prerequisite:

Elec.-Comp. Eng. 270 or I.&O.E. 473 or Comp. & Comm. Sci. 374. (3).Application of several software packages and display devices for engineering problem solving

and production of computer animated films. Use of Computek, Tektronix, and PDP graphics

terminals for electrical circuit design, interactive data smoothing, production of engineering

graphs, etc. POLYGRAPHICS and BEFLIX computer animation packages and their use in MTS.Production of 2 or 3 films using graphics terminals.

464( A.&O.Scl. 464). Upper Atmospheric Science. Prerequisite: senior or graduate standing

in a physical science or engineering. I. (3).An introduction to physical processes in the upper atmosphere; density, temperature, composition,and winds; atmospheric radiation transfer processes and heat balance; the ionosphere; rocket and


471. Automatic Control Systems. Prerequisite: Math. 216. I and II. (3).Transient and steady-state analysis of linear control systems; transfer function and state-space

description of control systems; stability analysis and synthesis methods; application to the design

of autopilots and other modem control systems; introduction to nonlinear control systems and

phase plane analysis.

472(C.I.C.E. 450) (Elec.-Comp. Eng. 450). Fundamentals of Control Systems. Prerequisite:Mech. Eng. 240, Elec.-Comp. Eng. 310, or Elec-Comp. Eng. 355, and senior standing. Iand II. (3).

Concept and importance of control systems. Control system descriptions: state variable and

transfer function representations. System performance and design criteria: stability, sensitivity,time response. Concept of feedback. Time response of linear control systems. Use of Hurwitz,root-locus, Nyquist and Bode methods for analysis and synthesis of linear control systems. Notopen to students with credit for Aero. Eng. 471.

473<C.I.C.E. 451) (Elec.-Comp. Eng. 451). Control Systems Laboratory. Prerequisite:CJ.C.E. 450 or Aero. Eng. 471. (2).

Introduction to control system simulation and design. Experiments with physical systems.

IIlustration of basic control principles. Design examples and the use of computer design aids.

481. Airplane Design. Prerequisite: senior standing. I. (4).

Power-required and power-available characteristics of aircraft on a comparative basis, calculation

of preliminary performance, stability, and control characteristics. Design procedure, including

layouts and preliminary structural design. Subsonic and supersonic designs. Emphasis on design

techniques and systems approach. Lectures and laboratory.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

I28 / AEROSPACE ENGINEERING


(4).Design techniques and projects for geophysical, environmental, and earth resources surveys.Aircraft, sounding rocket, and balloon instruments and payloads as well as vehicle characteristics,

and performance are considered. Student projects bring together in a unified concept components

for sensing (remote and in situ), telemetering, tracking, performance, safety, and data processing.

483. Aerospace System Design. Prerequisite: senior standing. U. (4).


systems, spacecraft systems, communications, data processing, and project management. Lectures and laboratory.

484. Computer Aided Design. Prerequisites: Aero. Eng. 4l4 and senior standing. I. (4).

Computer generation of geometric models. Calculation of design parameters. Finite element

modeling and analysis. Each student will complete a structural component design project usingindustry standard applications software.


5l0XAppl. Mech. 5I0XMech. Eng. 557). Finite Element Methods in Mechanics I. Prerequisite:Aero. Eng. 4l4(Appl. Mech. 4l4) or Appl. Mech. 4l3. I. (3).

Development of the finite element method with emphasis on energy principles. Virtual work.Potential energy. Application to line elements, beams, plane stress, plane strain, and three-


514(Appl. Mech. 5I4). Foundations of Structural Mechanics I. Prerequisite: Aero. Eng.4l4. (3).

Elements of the analysis of structures. Includes plates of various shapes, loading and boundaryconditions, effects of in-plane loading; shells of revolution, cylindrical shells, bending and

membrane theories; plastic analysis of structures, beams, frames, plates; plastic collapse

mechanism. Applications of aerospace interest.

5I5(Appl. Mech. 5I5). Foundations of Structural Mechanics II. Prerequisite: Aero. Eng.5l4. (3).

Behavior of structures in a thermal environment, heat conduction, aerodynamic heating of high

speed vehicles, thermal stresses and deflections, thermal instabilities, discussion of material

properties at elevated temperature. Elements of the theory of linear viscoelasticity.

5I8(Appl. Mech. 5I8). Theory of Elastic Stability I. Prerequisite: Appl. Mech. 5ll. I and

II. (3).Elastic and inelastic buckling of bars and frameworks; variational principles and numerical

solutions; lateral buckling of beams. Instability of rings.

520. Gasdynamics I. Prerequisite: Aero. Eng. 420. (3).Gasdynamics at an intermediate level: Thermodynamics; the conservation equations; vorticitytheorems; unsteady one-dimensional flow; the method of characteristics; stationary and movingshock waves; two-dimensional steady flow including method of small perturbations.

52I. Experimental Gasdynamics. Prerequisite: Aero. Eng. 330 and 420. (3).Experimental methods in modem gasdynamics; physical principles and interpretation. Shoppractice and theory of instrument design: mechanics, electronics, and optics. Measurement of

velocity, pressure, density, temperature, composition, energy and mass transfer in fluids and

plasmas. Transducers and laboratory instrumentation in gasdynamic research.

522. Gasdynamics II. Prerequisite: Aero. Eng. 520. (3).The Navier-Stokes equations, including elementary discussion of tensors; exact solutions.Laminar boundary-layer theory; asymptotic concepts; solutions for incompressible boundary

layers. Compressible boundary layers; special solutions; transformation of equations; heat

transfer in forced and free convection. Introduction to the mechanics of turbulence; Reynoldsstresses; turbulent boundary layers.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


529. Introduction to Energy Transfer. Prerequisite: Aero. Eng. 330. (3).A survey of energy transfer processes including unsteady heat conduction, convection in

non-reactive and reactive flows, and radiation. Aerospace applications, including re-entry

heating, ablation, rocket nozzle cooling, radiative transfer, satellite heating, convection in

dissociated flows.

530. Propulsion III. Prerequisite: Aero. Eng. 430. (3).Continuation of Aero. Eng. 430. Further treatment of aircraft engine performance, includingoff-design operation, and study of selected problems in the field of propulsion.

532. Introduction to Gaskinetics and Real Gas Effects. Prerequisite: Aero. Eng. 420. (3).A study of some modern topics of flow problems not covered in the traditional gasdynamics ofideal gases: concepts of gaskinetics, aerodynamics of free molecules, shock transition layer, real

gas effects, high temperature effects, multicomponent flows, etc.

533. Combustion Processes. Prerequisite: Aero. Eng. 320. (3).This course covers the fundamentals of combustion processes and applications to propulsion,high energy flows, pollutant generation, combustion systems, and fire and explosion phenomena.

Topics covered include thermochemistry, chemical kinetics, laminar flame propagation, detona

tions and explosions, flammability and ignition, spray combustion, and the use of computer

techniques in combustion problems.

535. Rocket Propulsion. Prerequisite: Aero. Eng. 430. (3).Analysis and performance of liquid and solid propellant rocket powerplants; propellantthermochemistry, heat transfer, system considerations, advanced rocket propulsion techniques.

540<Appl. Mech. 540). Intermediate Dynamics. Prerequisite: Mech. Eng. 240. I. (4).Kinematics of motion, particle dynamics, Lagrange's equations. Rigid body dynamics includingEuler's equations, the Poinsot construction, spin stabilization, the rotation matrix. Vibrations ofcoupled systems, orthogonality relationships, generalized co-ordinates and generalized system

parameters.

542. Astrodynamics I. Prerequisite: Aero. Eng. 340. I. (3).The study of motion of spacecraft in a vacuum and in the atmosphere with emphasis on

preliminary mission planning. Analysis of trajectories in suborbital, orbital, lunar, and interplane

tary operations. Aerodynamic forces and heating characteristics and their effect on the selection

of flight paths during entry into planetary atmospheres.

543. Structural Dynamics. Prerequisite: Aero. Eng. 414 or 540. (3).Natural frequencies and mode shapes of elastic bodies. Nonconservative elastic systems.

Structural and viscous damping. Influence coefficient methods for typical flight structures.

Response of structures to random and shock loads. Lab demonstration.

544. Aeroelasticity. Prerequisite: Aero. Eng. 414 or 540. (3).An introduction to aeroelasticity. Vibration and flutter of elastic bodies exposed to fluid flow.Static divergence and flutter of airplane wings. Flutter of flat plates and thin walled cylinders at

supersonic speeds. Oscillations of structures due to vortex shedding.

545. Principles of Vertical Take-Off and Landing Aircraft. Prerequisite: preceded or

accompanied by Aero. Eng. 420. (3).

Introduction to helicopter performance, aerodynamics, stability and control, vibration and flutter.

Other V/STOL concepts of current interest.

546(Appl. Mech. 547). Advanced Dynamics. Prerequisite: Aero. Eng. 540 or Appl. Mech.

440. <3).

Hamilton's equations, canonical transformations, and Hamilton-Jacobi theory. Applications to

orbital problems. General perturbation theory. Introduction to special relativity.

548. Astrodynamics II. Prerequisite: Aero. Eng. 542. (3).

Orbit determination. Systems of canonical equations. Perturbation theory with applications to the


Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

I30 / AEROSPACE ENGINEERING

549(Appl. Mech. 549) (Mech. Eng. 549). Random Vibrations of Mechanical Systems.Prerequisite: Mech. Eng. 240. (3).

Random mechanical inputs; wind buffeting; earthquakes; surface irregularities. Engineeringapplications include response of linear spring-mass system and an elastic beam to single and

multiple random loading. Failure theories. Necessary concepts such as ensemble averages,

correlation functions, stationary and ergodic random processes, power spectra, are developed

neurotically.

550(C.I.C.E. 500). Linear Dynamical Systems. Prerequisite: C.I.C.E. 40l. or Math. 404 and

Math. 4l7: and Elec.-Comp. Eng. 300 or Math. 448. I and U. (3).Models of dynamical systems and their linear specializations: difference and differential equations,

general axiomatic formulations. Rigorous treatment of numerous system concepts: linearity, time

invariance. causality, input-output representations, controllability, observability, equivalence,canonical decomposition, minimal realizations, inverse systems, stability.

552(C.I.C.E. 5I2). Probability and Random Processes. Prerequisite: C.I.C.E. 4l2 orgraduate standing. I and II. (4).

Rigorous study of the basic concepts of probability theory: sample spaces, probability axioms,

random variables, probability distribution functions, statistical averages. Introduction to random

processes: stationarity, covariance and correlation functions, Poisson processes, Gaussian processes.

Recitation. C.I.C.E. students may not receive graduate credit for both C.I.C.E. 4I2 and C.I.C.E.5l2.

553(C.I.C.E. 5I5). Continuous State Stochastic Processes. Prerequisite: C.I.C.E. 5l2.n. (3>.

Gaussian processes. Correlation functions. Stationary processes; ergodic properties and spectral




565(Appl. Mech. 565). Optimal Structural Design. Prerequisite: Aero. Eng. 4l4 and 350.

I. (3).Optimal design of structural elements (bars, trusses, frames, plates, sheets) and systems;

variational formulation for discrete and distributed parameter structures; sensitivity analysis;

optimal material distribution and layout; design for criteria of stiffness, strength, buckling, and

dynamic response.

570. Guidance and Navigation of Aerospace Vehicles. Prerequisite: a course in feedbackcontrol. I. (3).

Principles of space vehicle, homing and ballistic missiles guidance systems in two and three

dimensions. Explicit, linear perturbation, and velocity-to-be gained guidance modes. Mechanization by inertial and other means, including strapped-down and stable-platform inertial systems.Celestial navigation procedures with deterministic and redundant measurements. Application ofKalman filtering to recursive navigation theory.

571(C.I.C.E. 552). Sampled Data Control Systems. Prerequisite: C.I.C.E. 40l, or Math.404 and Math. 4l7; and C.I.C.E. 450 or Aero. Eng. 47l. II. (3).

Technological reasons for sampling. Sampling, extrapolation, and interpolation processes;

quantizing effects. The z-transform and its application to mixed data systems: steady state and

transient response; stability determination. Compensator design; realization by digital computers.State space methods for analysis and design.

572(C.I.C.E. 550). Nonlinear Control Systems. Prerequisites: C.I.C.E. 40l. or Math. 404

and Math. 4l7; and C.I.C.E. 450 or Aero. Eng. 47l. I and II. (3).Modeling of nonlinear control systems by state and operator descriptions. Nonlinear phenomena:limit cycles, sliding solutions, subharmonics, jump phenomena, domain of stability. Use of phase

plane techniques, describing functions, Liapunov theory and frequency response methods (circleand Popov criteria) for analyzing and designing nonlinear control systems.

574. Control of Aircraft, Missiles, and Space Vehicles. Prerequisite: preceded or accompanied by C.I.C.E. 550. II. (2).

Analysis and synthesis of autopilots for aircraft and cruise-type missiles. Design of thrust-vector

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

AEROSPACE ENGINEERING I I3I

control systems including effects of elastic structures and fuel sloshing. Attitude control systemsfor space vehicles; mechanization using jet thrusters and inertia wheels; gravity gradientmoments.

575. Optimization of Space Trajectories. Prerequisite: permission of instructor. II. (3).Necessary and sufficient conditions for ordinary extremum and variational problems, withemphasis on the problem of Bolza. Applications of the calculus of variations to optimal space

trajectories. Problems with control and state variable inequality constraints. Iterative computa

tional methods for two-point boundary- value problems, including the gradient method. Newton'smethod, and quasilinearization.

576XC.I.C.E. 540). Optimal Control. Prerequisites: C.I.C.E. 40l. or Math 404 and Math.4l7. n. (3).

Formulation of optimal control problems. Constrained minimization problems in finite dimen

sional space; necessary conditions for optimality and their application to discrete-time optimalcontrol problems. Dynamic programming, Hamilton-Jacobi theory, the Pontryagin necessary

conditions. Applications to time and fuel optimal systems and the linear-quadratic problem.

Examples taken from a variety of fields. Introduction to computational considerations.

577(CJ.C.E. 545)(I.&O.E. 511XMath. 562). Continuous Optimization Methods. Prerequisites: Math. 4I7 or Math. 4l9. I and II. (3).

Survey of continuous optimization problems. Unconstrained optimization problems: unidirec

tional search techniques; gradient, conjugate direction, quasi-Newton methods. Introduction to

constrained optimization using techniques of unconstrained optimization through penaltytransformations, augmented Lagrangians, and others. Discussion of computer programs forvarious algorithms.

578(C.I.C.E. 542). Applied Optimal Estimation. Prerequisites: C.I.C.E. 40l, 4l2, 450.

n. (3).Formulation of optimal estimation problems. Least squares, and generalized least squares

techniques. Recursive techniques and Kalman filtering for linear discrete time systems. Exten

sions to continuous time systems, steady state filtering, nonlinear filtering, numerical difficulties,

prediction, and smoothing. Parameter and state identification techniques. The linear-quadratic-

gaussian optimal control problems.


596. Aurora and Airglow. Prerequisite: permission of instructor. II. (3).Morphology and physics of the aurora and airglow. Emission spectra in the aurora and their

atomic and molecular origin; proton aurora; metastable excitation; calculation of emission

profiles. Night-and day-glow; pre-dawn and post-twilight enhancements; mid-latitude red arc;

excitation mechanisms.

6I0(Appl. Mech. 6I0). Finite Element Methods in Mechanics II. Prerequisite: Aero. Eng.5l0(Appl. Mech. 5l0) (Mech. Eng. 557). U. (3).

Advanced topics in finite element theory. Plates, shells, large deflections, stability, plasticity,dynamics. Iterative methods for nonlinear problems. Solution of field problems for fluid flow and



boundary layers; boundary layer stability and transition to turbulence; turbulent boundary layers,

wakes, and jets.

62I. Dynamics of Compressible Fluids. Prerequisite: Aero. Eng. 520. (3).

Theory of characteristics; shock-wave phenomena; interaction problems; hodograph transformation;

transonic flow.

627. Continuum Theory of Fluids. Prerequisite: Aero. Eng. 520. (3).Physical concepts underlying the flow of fluids acted upon by stresses arising from viscosity and

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


from electromagnetic and gravity fields. Invariant analysis of stress-strain relations. MaxweII'sequations, analysis of electromagnetic stresses and energy dissipation in moving media, the

equations of motion and energy in a moving fluid, and some solutions of the complete equations.

628. Statistical Theory of Fluids. Prerequisite: Aero. Eng. 532. II.(3).Statistical theory of flow from the viewpoint of the Boltzmann equation. The Chapman-Enskogsolution for the transport phenomena. Rarefied gas dynamics. Studies of the random fluctuation

phenomena by means of the Fokker-Planck equation, the generalized harmonic analysis ofWiener-Khintchine. Brownian motion, turbulent diffusion, etc. Irreversible thermodynamics and

Onsager's reciprocal relation.

632. Gas Flows with Chemical Reactions. Prerequisite: Aero. Eng. 532. 620. (3).Thermodynamics of gas mixtures, chemical kinetics, conservation equations for multicomponent

reacting gas mixtures. Deflagration and detonation waves. Nozzle flows and boundary layers

with reaction and diffusion.

651(C.I.C.E. 501). Function Space Methods in System Theory. Prerequisites: C.I.C.E.401. H. (3).

Introduction to the description and analysis of systems using function analytic methods. Metric

spaces, normed linear spaces, Hilbert spaces, resolution spaces. Emphasis on using these

concepts in systems problems.

652(C.I.C.E. 610). Theory or Stochastic Processes. Prerequisites: C.I.C.E. 515. (3).Measure theoretic treatment of stochastic processes. Analysis and representation of various

stochastic processes using function analytic concepts. Wiener processes, martingales, diffusion

processes. Stochastic integrals, introduction to stochastic differential equations and stochastic

calculus.

653(C.I.C.E. 612). Estimation Theory. Prerequisites: C.I.C.E. 522. II. (3).Representations of stochastic processes for statistical estimations. Least squares and linear

unbiased minimum variance estimators. Bayes, min-max, maximum likelihood of posteriori and

maximum likelihood estimators. Recursive filtering, prediction, and interpolation. Applications

to control and communications.

673(Elec.-Comp. Eng. 673) (Nuc. Eng. 673). Topics in Theoretical Plasma Physics. Pre

requisite: Nuc. Eng. 571 or Elec.-Comp. Eng. 580 or Aero. Eng. 726. I and II. (3). This

course may be taken for credit more than once.


Specific content will vary from year to year. Representative topics include: studies of weakly

ionized plasmas with applications to gas lasers; space plasmas; laser fusion plasmas; and

nonlinear plasma dynamics and plasma turbulence.

676(C.I.C.E. 640). Theory of Optimal Control. Prerequisites: C.I.C.E. 540 or Aero.

Eng. 575. (3).General theoretical questions in optimal control: existence of optimal controls, derivation of

necessary and sufficient conditions for optimality. Selected special topics: singular control, state

constraints, min-max criteria, systems described by partial differential equations, the second

variation. Examples and applications of the theory.




equations for a plasma; instabilities; transport phenomena and derivation of the magnetohydrody-

namic equations.



Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle







990. DisserUtfon/Pre-Candidate. I and II (2-8); IHa and \Ub. (1-4).Election for dissertation work by doctoral student not yet admitted to status as a Candidate.

The defense of the dissertation, that is, the final oral examination must be held under a fullterm candidacy enrollment.


doctoral candidate. I and II (8); IIia and \Ub. (4).Election for dissertation work by doctoral student who has been admitted to status as a Candidate.

The defense of the dissertation, that is, the final oral examination must be held under a fullterm candidacy enrollment.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:2

8 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:3

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle





AEROSPACE ENGINEERING I l25


Department Office: 302 Aerospace Engineering Building, phone (3I3) 764-33I0See Page l24 for statement on Course Equivalence.

I00. Introduction to Flight. (2).An introduction to the physical principles of flight within the atmosphere and in space, to the

major historical developments in the conquest of air and space, and to the current state of

aerospace developments and their role in national and world affairs.

200. General Aeronautics and Astronautics. Prerequisite: Physics l40, preceded or accompa

nied by Eng. l03. I and II. (2).Introduction to aerospace engineering. Elementary problems designed to orient the student in the



300. Elements of Space Science and Technology. Prerequisite: Math. 2I6; Physics 240. (3).Scientific and technological aspects of current space flights, mission goals, the space environment,



30I. Laboratory I. Prerequisite: preceded or accompanied by EECS 3l4. I and II. (2).


principles of electronics, circuit analysis, transducers, modern laboratory instrumentation,

experimental methods, and data analysis. Experiments involve simple measurement and instru

mentation problems.

302. Laboratory II. Prerequisite: Aero. Eng. 30l. I and II. (2).Continuation of the material in Aero. Eng. 30I.

3I4. Structural Mechanics I. Prerequisite: Mech. Eng. 2ll. I and II. (3).Review of plane states of stress and strain; basic equations of plane elasticity and selected

problems; failure criteria and applications; energy principles of structural theory; thin-walledbeam theory.




330. Aerodynamics II. Prerequisite: Aero. Eng . 320 or introductory course in fluid mechanics.

I and II. (3).Second part of an aerodynamics sequence designed to study the fundamental principles and their

applications; viscous effects in laminar and turbulent flows; boundary layer theory; concepts of

instability and transition to turbulent flow; flows under the influence of gravitational and

electromagnetic forces.

340. Mechanics of Flight. Prerequisite: Aero. Eng. 200, Mech. Eng. 240. I and II. (3).Mechanics of a particle applied to the analysis of vehicle flight paths. Rigid body mechanics

applied to translational and rotational vehicle motion. Analysis of vehicle motion and static and

dynamic stability using perturbation theory.

350(Math. 350). Aerospace Engineering Analysis. Prerequisite: Math. 2I6. I and II. (3).Formulation and solution of some of the elementary initial- and boundary-value problems

relevant to aerospace engineering. Application of Fourier series, separation of variables, and

vector analysis to problems of forced oscillations, wave motion, diffusion, elasticity, and

perfect-fluid theory.

380. Undergraduate Seminar. Prerequisite: junior standing. (l).A series of seminars by noted outside speakers designed to acquaint undergraduates with both

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:3

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


current problems and state of the art of the aerospace industry. Will involve a short term project or

paper pertinent to one of the seminar topics.


Individual study of specialized aspects of aerospace engineering.

411(Appl. Mech. 411)(Civ. Eng. 411)(Nav. Arch. 411). Finite Element Applications. Prerequisite: Eng. 103. Mech. Eng. 211. I. <3).

The application of user oriented finite element computer programs for solving practical structuralmechanics problems of frames, 2-D and 3-D solids, plates, shells, etc., and displaying the

solutions graphically. Students learn to prepare input data and interpret results. A shortintroduction to the underlying theory is also presented.

414(Appl. Mech. 414). Structural Mechanics II. Prerequisite: Aero. Eng. 314. I and II<3).

Introduction to plate theory. Stability of structural elements; columns and beam columns; plate in

compression and shear; secondary instability of columns. Introduction to matrix methods ofdeformation analysis; structural dynamics.

416. Theory of Plates and Shells. Prerequisite: Mech. Eng. 211, Math. 450 or Aero. Eng.350. (3).

Linear elastic plates, linear theory of membranes. Bending of axisymmetric and non-axisymmetriclinear shells, vibrations of shells, finite element techniques for solving plates and shell

problems.

420. Aerodynamics III. Prerequisite: Aero. Eng. 320. and Aero. Eng. 350 or Math. 450;

preceded or accompanied by Aero. Eng. 330. I and II. (3).Third part of an aerodynamic sequence designed to study the fundamental principles and their



423. Aero-Acoustics. Prerequisite: Aero. Eng. 320 or a course in compressible flow. (3).Principles of generation, perception, and abatement of sound generated by fluid flows. Elemen

tary acoustics; acoustical response of the human ear. Theory and results of measurement of

sound generated by explosions, sonic booms, jets, boundary layers, and flow excitedstructural vibrations. Qualitative assessment of techniques and effectiveness of noise abatement

procedures.

424. Applied Aerodynamics. Prerequisite: Aero. Eng. 420. (3).

Topics related to flow about aircraft wings and bodies and the resulting aerodynamic forces at

subsonic, transonic and supersonic speeds. Potential flows, boundary layers, shock waves,

separation, transition, turbulence, effects of Mach and Reynolds numbers. Discussion and

explanation of analytical methods, numerical methods, and experimental results. Selected other

applications.

430. Propulsion II. Prerequisite: Aero. Eng. 320. I and II. (3).

Performance and analysis of flight-propulsion systems including the reciprocating engine-

propeller, turbojet, turboprop, ramjet, and rocket.

439. Aircraft Propulsion Laboratory. Prerequisite: Aero. Eng. 320. (2).

Series of experiments designed to illustrate the general principles of propulsion and to

introduce the student to certain experimental techniques in the study of actual propulsive

devices, using full-scale or reduced models of the pulsejet, turbojet, ramjet, and rocket

motors.


performance parameters, and performance indices. The aircraft performance problem; flight

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:3

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


envelope, aerodynamic approximations, available propulsion systems; takeoff, landing, climb,

and range performance. Modem performance optimization techniques. Applications to automobile,

high-speed train, and space vehicle performance analysis.

447. Flight Testing. Prerequisite: Aero. Eng. 340. (2).

Theory and practice of obtaining flight-test data on performance and stability of airplanes from

actual flight tests. No laboratory fee will be charged, but a deposit covering student insurance and

operating expense of the airplane will be required.

452(EECS 401). Probabilistic Methods in Engineering. Prerequisite: EECS 300 or Math.

448. I and II. (3).

Basic concepts of probability theory. Random variables: discrete, continuous, and conditional

probability distributions, averages, independence. Introduction to discrete and continuous ran

dom processes: wide sense stationarity, correlation, spectral density. C.I.C.E. students may not

receive graduate credit for both EECS 401 and 501.

455(EECS 488). Computer Graphics Application. Prerequisite: EECS 280 or l.&O.E. 473

or EECS 383. (3).

Application of several software packages and display devices for engineering problem solving

and production of computer animated films. Use of Computek, Tektronix, and PDP graphics

terminals for electrical circuit design, interactive data smoothing, production of engineering

graphs, etc. POLYGRAPHICS and BEFLIX computer animation packages and their use in MTS.

Production of 2 or 3 films using graphics terminals.

464(A.&O.Sri. 464). Upper Atmospheric Science. Prerequisite: senior or graduate standing

in a physical science or engineering. I. (3).

An introduction to physical processes in the upper atmosphere; density, temperature, composition,

and winds; atmospheric radiation transfer processes and heat balance; the ionosphere; rocket and


471. Automatic Control Systems. Prerequisite: Math. 216. I and II. (3).

Transient and steady-state analysis of linear control systems; transfer function and state-space

description of control systems; stability analysis and synthesis methods; application to the design

of autopilots and other modern control systems; introduction to nonlinear control systems and

phase plane analysis.

472(EECS 460). Fundamentals of Control Systems. Prerequisite: Mech. Eng. 240, EECS 310

or EECS 360. and senior standing. I and II. (3).

Concept and importance of control systems. Control system descriptions: state variable and

transfer function representations. System performance and design criteria: stability, sensitivity,

time response. Concept of feedback. Time response of linear control systems. Use of Hurwitz,

root-locus, Nyquist and Bode methods for analysis and synthesis of linear control systems. Not

open to students with credit for Aero. Eng. 471.

473(EECS 461). Control Systems Laboratory. Prerequisite: EECS 460 or Aero. Eng.

471. (2).

Introduction to control system simulation and design. Experiments with physical systems.

Illustration of basic control principles. Design examples and the use of computer design aids.

481. Airplane Design. Prerequisite: senior standing. I. (4).

Power-required and power-available characteristics of aircraft on a comparative basis, calculation

of preliminary performance, stability, and control characteristics. Design procedure, including

layouts and preliminary structural design. Subsonic and supersonic designs. Emphasis on design

techniques and systems approach. Lectures and laboratory.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:3

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle



(4).

Design techniques and projects for geophysical, environmental, and earth resources surveysAircraft, sounding rocket, and balloon instruments and payloads as well as vehicle characteristics,

and performance are considered. Student projects bring together in a unified concept componentsfor sensing (remote and in situ), telemetering, tracking, performance, safety, and data processing.

483. Aerospace System Design. Prerequisite: senior standing. II. (4).


systems, spacecraft systems, communications, data processing, and project management. Lectures and laboratory.

484. Computer Aided Design. Prerequisites: Aero. Eng. 414 and senior standing. I. (4).Computer generation of geometric models. Calculation of design parameters. Finite elementmodeling and analysis. Each student will complete a structural component design project usingindustry standard applications software.


SlOXAppl. Mech. SlOMMech. Eng. 557). Finite Element Methods in Mechanics I. Prerequisite:Aero. Eng. 414(Appl. Mech. 414) or Appl. Mech. 413. I. (3).

Development of the finite element method with emphasis on energy principles. Virtual work.Potential energy. Application to line elements, beams, plane stress, plane strain, and three-


514(Appl. Mech. 514). Foundations of Structural Mechanics I. Prerequisite: Aero. Eng.414. (3).

Elements of the analysis of structures. Includes plates of various shapes, loading and boundaryconditions, effects of in-plane loading; shells of revolution, cylindrical shells, bending and

membrane theories; plastic analysis of structures, beams, frames, plates; plastic collapsemechanism. Applications of aerospace interest.

515(Appl. Mech. 515). Foundations of Structural Mechanics II. Prerequisite: Aero. Eng.514. (3).

Behavior of structures in a thermal environment, heat conduction, aerodynamic heating of high

speed vehicles, thermal stresses and deflections, thermal instabilities, discussion of material

properties at elevated temperature. Elements of the theory of linear viscoelasticity.

518(Appl. Mech. 518). Theory of Elastic Stability I. Prerequisite: Appl. Mech. 511. I and

H. (3).Elastic and inelastic buckling of bars and frameworks; variational principles and numerical

solutions; lateral buckling of beams. Instability of rings.

520. Gasdynamics I. Prerequisite: Aero. Eng. 420. (3).

Gasdynamics at an intermediate level: Thermodynamics; the conservation equations; vorticitytheorems; unsteady one-dimensional flow; the method of characteristics; stationary and movingshock waves; two-dimensional steady flow including method of small perturbations.

521. Experimental Gasdynamics. Prerequisite: Aero. Eng. 330 and 420. (3).

Experimental methods in modern gasdynamics; physical principles and interpretation. Shop

practice and theory of instrument design: mechanics, electronics, and optics. Measurement ofvelocity, pressure, density, temperature, composition, energy and mass transfer in fluids and

plasmas. Transducers and laboratory instrumentation in gasdynamic research.

522. Gasdynamics II. Prerequisite: Aero. Eng. 520. (3).The Navier-Stokes equations, including elementary discussion of tensors; exact solutions.

Laminar boundary-layer theory; asymptotic concepts; solutions for incompressible boundarylayers. Compressible boundary layers; special solutions; transformation of equations; heat

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:3

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


transfer in forced and free convection. Introduction to the mechanics of turbulence; Reynoldsstresses; turbulent boundary layers.

523. Numerical Methods in Fluid Dynamics I. Prerequisites: Aero. Eng. 420 or equivalent.

I. (3).

Basic mathematical ideas needed for computational fluid dynamics, finite-difference approximations

to partial differential equations, applications to model equations for fluid dynamics.

529. Introduction to Energy Transfer. Prerequisite: Aero. Eng. 330. (3).A survey of energy transfer processes including unsteady heat conduction, convection in

non-reactive and reactive flows, and radiation. Aerospace applications, including re-entry

heating, ablation, rocket nozzle cooling, radiative transfer, satellite heating, convection in

dissociated flows.

530. Propulsion III. Prerequisite: Aero. Eng. 430. (3).Continuation of Aero. Eng. 430. Further treatment of aircraft engine performance, includingoff-design operation, and study of selected problems in the field of propulsion.

532. Introduction to Gaskinetics and Real Gas Effects. Prerequisite: Aero. Eng. 420. (3).A study of some modem topics of flow problems not covered in the traditional gasdynamics ofideal gases: concepts of gaskinetics, aerodynamics of free molecules, shock transition layer, real

gas effects, high temperature effects, multicomponent flows, etc.

533. Combustion Processes. Prerequisite: Aero. Eng. 320. (3).

This course covers the fundamentals of combustion processes and applications to propulsion,high energy flows, pollutant generation, combustion systems, and fire and explosion phenomena.

Topics covered include thermochemistry, chemical kinetics, laminar flame propagation, detona

tions and explosions, flammability and ignition, spray combustion, and the use of computer

techniques in combustion problems.

535. Rocket Propulsion. Prerequisite: Aero. Eng. 430. (3).

Analysis and performance of liquid and solid propellant rocket powerplants; propellant

thermochemistry, heat transfer, system considerations, advanced rocket propulsion techniques.

540( Appl. Mech. 540). Intermediate Dynamics. Prerequisite: Mech. Eng. 240. I. (4).

Kinematics of motion, particle dynamics, Lagrange's equations. Rigid body dynamics includingEuler's equations, the Poinsot construction, spin stabilization, the rotation matrix. Vibrations ofcoupled systems, orthogonality relationships, generalized co-ordinates and generalized system

parameters.

541. Computational Dynamics. Prerequisite: Aero. Eng. 540. I. (3).Formulation of dynamics problems for computer solution. Kinematic preliminaries. Matrixand dyadic notation. Constraints, generalized coordinates, and quasi-coordinates. Generalized

speeds. Rigid and flexible multi-body dynamics. Computational efficiency.

542. Astrodynamics I. Prerequisite: Aero. Eng. 340. I. (3).The study of motion of spacecraft in a vacuum and in the atmosphere with emphasis on

preliminary mission planning. Analysis of trajectories in suborbital, orbital, lunar, and interplane

tary operations. Aerodynamic forces and heating characteristics and their effect on the selection

of flight paths during entry into planetary atmospheres.

543. Structural Dynamics. Prerequisite: Aero. Eng. 414 or 540. (3).

Natural frequencies and mode shapes of elastic bodies. Nonconservative elastic systems.

Structural and viscous damping. Influence coefficient methods for typical flight structures.

Response of structures to random and shock loads. Lab demonstration.

544. Aeroelasticity. Prerequisite: Aero. Eng. 414 or 540. (3).An introduction to aeroelasticity. Vibration and flutter of elastic bodies exposed to fluid flow.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:3

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


Static divergence and flutter of airplane wings. Flutter of flat plates and thin walled cylinders at

supersonic speeds. Oscillations of structures due to vortex shedding.

545. Principles of Vertical Take-Off and Landing Aircraft. Prerequisite: preceded or

accompanied by Aero. Eng. 420. (3).Introduction to helicopter performance, aerodynamics, stability and control, vibration and flutter.Other V/STOL concepts of current interest.

546(Appl. Mech. 547). Advanced Dynamics. Prerequisite: Aero. Eng. 540 orAppl. Meeh440. <3).

Hamilton's equations, canonical transformations, and Hamilton- Jacobi theory. Applications to

orbital problems. General perturbation theory. Introduction to special relativity.



549(Appl. Mech. 549) (Mech. Eng. 549). Random Vibrations of Mechanical Systems.Prerequisite: Mech. Eng. 240. (3).

Random mechanical inputs; wind buffeting; earthquakes; surface irregularities. Engineeringapplications include response of linear spring-mass system and an elastic beam to single and

multiple random loading. Failure theories. Necessary concepts such as ensemble averages,

correlation functions, stationary and ergodic random processes, power spectra, are developedheuristically.

550(EECS 560). Linear Dynamical Systems. Prerequisite: EECS 400, or Math. 404 andMath. 417; and EECS 300 or Math. 448. I and II. (3).

Models of dynamical systems and their linear specializations: difference and differential equations,general axiomatic formulations. Rigorous treatment of numerous system concepts: linearity, time

invariance, causality, input-output representations, controllability, observability, equivalence,canonical decomposition, minimal realizations, inverse systems, stability.

552(EECS 501). Probability and Random Processes. Prerequisite: EECS 401 or graduatestanding. I and II. (4).

Rigorous study of the basic concepts of probability theory: sample spaces, probability axioms,

random variables, probability distribution functions, statistical averages. Introduction to random

processes: stationanty , covariance and correlation functions, Poisson processes, Gaussian processes.

Recitation. C.I.C.E. students may not receive graduate credit for both EECS 401 and EECS 501.

553(EECS 502). Continuous State Stochastic Processes. Prerequisite: EECS 501. n. (3).Gaussian processes. Correlation functions. Stationary processes; ergodic properties and spectral




565(Appl. Mech. 565). Optimal Structural Design. Prerequisite: Aero. Eng. 414 and 350.

I. (3).

Optimal design of structural elements (bars, trusses, frames, plates, sheets) and systems:

variational formulation for discrete and distributed parameter structures; sensitivity analysis;

optimal material distribution and layout; design for criteria of stiffness, strength, buckling, and

dynamic response.

570. Guidance and Navigation of Aerospace Vehicles. Prerequisite: a course in feedbackcontrol. I. (3).

Principles of space vehicle, homing and ballistic missiles guidance systems in two and three

dimensions. Explicit, linear perturbation, and velocity-to-be gained guidance modes. Mechanization by inertial and other means, including strapped-down and stable-platform inertial systems.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:3

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

AEROSPACE ENGINEERING / 131

Celestial navigation procedures with deterministic and redundant measurements. Application ofKalman filtering to recursive navigation theory.

571(EECS 561). Sampled Data Control Systems. Prerequisite: EECS 400, or Math. 404

and Math. 417; and EECS 460 or Aero. Eng. 471. II. (3).Technological reasons for sampling. Sampling, extrapolation, and interpolation processes;

quantizing effects. The z-transform and its application to mixed data systems: steady state and

transient response; stability determination. Compensator design; realization by digital computers.

State space methods for analysis and design.

572(EECS 562). Nonlinear Control Systems. Prerequisites: EECS 400, or Math. 404

and Math. 417; and EECS 460 or Aero. Eng. 471. I and II. (3).Modeling of nonlinear control systems by state and operator descriptions. Nonlinear phenomena:

limit cycles, sliding solutions, subharmonics, jump phenomena, domain of stability. Use of phase

plane techniques, describing functions, Liapunov theory and frequency response methods (circleand Popov criteria) for analyzing and designing nonlinear control systems.

573. Real-Time Simulation of Dynamic Systems. Prerequisite: permission of instructor.

(J).High-speed simulation of systems described by ordinary differential equations with emphasis on

real-time applications and hardware-in-the-loop. Error analysis of numerical integration methods,

use of multiple frame rates, treatment of discontinuous nonlinearities, performance of D-A and

A-D converters. Examples include control systems, flexible structures, and aerospace vehicles.

574. Control of Aircraft, Missiles, and Space Vehicles. Prerequisite: A course in feedbackcontrol. I (J).

Analysis and synthesis of autopilots for aircraft. Design of thrust-vector control systems

including effects of elastic structures and fuel sloshing. Attitude control systems for space

vehicles; mechanization using jet thrusters and inertia wheels; gravity gradient moments.

575. Optimization of Space Trajectories. Prerequisite: permission of instructor. II. (3).Introduction to optimal control. Switching theory. Applications to aerospace trajectories: orbital

transfer and rendezvous, atmospheric reentry, aero-assisted transfer.

576(EECS 563). Optimal Control. Prerequisites: EECS 400, or Math. 404 and Math.417. II. (3).

Formulation of optimal control problems. Constrained minimization problems in finite dimen

sional space; necessary conditions for optimality and their application to discrete-time optimal

control problems. Dynamic programming, Hamilton-Jacobi theory, the Pontryagin necessary

conditions. Applications to time and fuel optimal systems and the linear-quadratic problem.

Examples taken from a variety of fields. Introduction to computational considerations.

577(EECS 505HI.&O.E. 511)(Math. 562). Continuous Optimization Methods. Prerequisites: Math. 417 or Math. 419. I and II. <3).

Survey of continuous optimization problems. Unconstrained optimization problems: unidirec

tional search techniques; gradient, conjugate direction, quasi-Newton methods. Introduction to

constrained optimization using techniques of unconstrained optimization through penaltytransformations, augmented Lagrangians, and others. Discussion of computer programs forvarious algorithms.

578(EECS 564). Applied Optimal Estimation. Prerequisites: EECS 400. 401, and 460. II. (3).Formulation of optimal estimation problems. Least squares, and generalized least squares

techniques. Recursive techniques and Kalman filtering for linear discrete time systems. Exten

sions to continuous time systems, steady state filtering, nonlinear filtering, numerical difficulties,

prediction, and smoothing. Parameter and state identification techniques. The linear-quadratic-

gaussian optimal control problems.

579. Control of Aerospace Structures. Prerequisites: Aero. Eng. 471, Aero. Eng. 414,

and Aero. Eng. 550. II. (3).

Equations of motion of controlled elastic structures; modal and finite element formulations; shape

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:3

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


control; active damping using feedback; application to control of flexible aircraft and flexible

space structures.


Individual study of specialized aspects of aerospace engineering. Primarily for graduates.

5%. Aurora and Airglow. Prerequisite: permission of instructor. II. (3).

Morphology and physics of the aurora and airglow. Emission spectra in the aurora and their

atomic and molecular origin; proton aurora; metastable excitation; calculation of emission

profiles. Night-and day-glow; pre-dawn and post-twilight enhancements; mid-latitude red arc;

excitation mechanisms.

610(Appl. Mech. 610). Finite Element Methods in Mechanics II. Prerequisite: Aero. Eng.510 (Appl. Mech. 510) (Mech. Eng. 557). II. (3).

Advanced topics in finite element theory. Plates, shells, large deflections, stability, plasticity,dynamics. Iterative methods for nonlinear problems. Solution of field problems for fluid flow and




621. Dynamics of Compressible Fluids. Prerequisite: Aero. Eng. 520. (3).

Theory of characteristics; shock-wave phenomena; interaction problems; hodograph transformation;

transonic flow.

623. Numerical Methods in Fluids Dynamics II. Prerequisites: Aero. Eng. 523 or equivalent.

preceded or accompanied by Aero. Eng. 520 and Aero. Eng. 522. II. (3).

Techniques for numerical calculation of boundary-layer flows, transonic potential flows, and

compressible rotational flows. Solution of the Navier-Stokes equations. Other topics such as grid

generation, turbulence modeling, etc.

627. Continuum Theory of Fluids. Prerequisite: Aero. Eng. 520. (3).

Physical concepts underlying the flow of fluids acted upon by stresses arising from viscosity and

from electromagnetic and gravity fields. Invariant analysis of stress-strain relations. Maxwell's

equations, analysis of electromagnetic stresses and energy dissipation in moving media, die

equations of motion and energy in a moving fluid, and some solutions of the complete equations.

628. Statistical Theory of Fluids. Prerequisite: Aero. Eng. 532. II.(3).Statistical theory of flow from the viewpoint of the Boltzmann equation. The Chapman-Enskogsolution for the transport phenomena. Rarefied gas dynamics. Studies of the random fluctuation

phenomena by means of the Fokker-Planck equation, the generalized harmonic analysis ofWiener-Khintchine. Brownian motion, turbulent diffusion, etc. Irreversible thermodynamics and

Onsager's reciprocal relation.

632. Gas Flows with Chemical Reactions. Prerequisite: Aero. Eng. 532. and 620. (3).Thermodynamics of gas mixtures, chemical kinetics, conservation equations for multicomponem

reacting gas mixtures. Deflagration and detonation waves. Nozzle flows and boundary layers

with reaction and diffusion.

651(EECS 600). Function Space Methods in System Theory. Prerequisite: EEC5 400.

II. (3).Introduction to the description and analysis of systems using function analytic methods. Metric

spaces, normed linear spaces, Hilbert spaces, resolution spaces. Emphasis on using these

concepts in systems problems.

652(EECS 602). Theory of Stochastic Processes. Prerequisite: EECS 502. (3).Measure theoretic treatment of stochastic processes. Analysis and representation of variousstochastic processes using function analytic concepts. Wiener processes, martingales, diffusion

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:3

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle


processes. Stochastic integrals, introduction to stochastic differential equations and stochastic

calculus.

653(EECS 603). Estimation Theory. Prerequisite: EECS 553. II. (3).

Representations of stochastic processes for statistical estimations. Least squares and linear

unbiased minimum variance estimators. Bayes. min-max, maximum likelihood of posteriori and

maximum likelihood estimators. Recursive filtering, prediction, and interpolation. Applications

to control and communications.

673(EECS 617) (Nuc. Eng. 673). Topics in Theoretical Plasma Physics. Prerequisite:Nuc. Eng. 571 or EECS 517 or Aero. Eng. 726. I and II. (3). This course may be

taken for credit more than once.


Specific content will vary from year to year. Representative topics include: studies of weakly

ionized plasmas with applications to gas lasers; space plasmas; laser fusion plasmas; and

nonlinear plasma dynamics and plasma turbulence.

676(EECS 663). Theory of Optimal Control. Prerequisites: EECS 563 or Aero. Eng. 575. (3).

General theoretical questions in optimal control: existence of optimal controls, derivation ofnecessary and sufficient conditions for optimality. Selected special topics: singular control, state

constraints, min-max criteria, systems described by partial differential equations, the second

variation. Examples and applications of the theory.

721. Turbulence. Prerequisite: Aero. Eng. 620. (3).

Physical and mathematical description of turbulence in boundary layers, wakes, jets, and behind


726. Introduction to Plasma Dynamics. Prerequisite: permission of instructor. (3).

Physical properties of a plasma; particle orbit theory; collective phenomena in a plasma; kinetic

equations for a plasma; instabilities; transport phenomena and derivation of the magnetohydrody-

namic equations.

729. Special Topics in Gasdynamics. Prerequisite: permission ofinstructor. (To be arranged).

Advanced topics of current interest.

740. Special Topics in Flight Dynamics and Control Systems. (To be arranged).





840. Seminar in Flight Dynamics and Control Systems. (To be arranged).


990. Dissertation/Pre-Candidate. I and II (2-8); Ma and 1IIfc. (1-4).Election for dissertation work by doctoral student not yet admitted to status as a Candidate.

The defense of the dissertation, that is, the final oral examination must be held under a full

term candidacy enrollment.


doctoral candidate. I and II (8); IIIa and \Ub. (4).Election for dissertation work by doctoral student who has been admitted to status as a Candidate.

The defense of the dissertation, that is, the final oral examination must be held under a full

term candidacy enrollment.

Genera

ted f

or

nhm

(U

niv

ers

ity o

f M

ichig

an)

on 2

01

5-0

9-3

0 1

9:3

2 G

MT /

htt

p:/

/hdl.handle

.net/

20

27

/mdp.3

90

15

02

16

56

45

2O

pen A

ccess

, G

oog

le-d

igit

ized

/

htt

p:/

/ww

w.h

ath

itru

st.o

rg/a

ccess

_use

#oa-g

oogle

College of Engineering : [catalog]. · 122/AEROSPACEENGINEERING AerospaceEngineering DepartmentOffice:302AerospaceEngineeringBuilding,phone(313)764-3310 SeePage121forstatementonCourseEquivalence.

Documents