16.360 Lecture 14 • Today Orthogonal coordinate systems 1. The Cartesian (rectangular) coordinate system 2. The cylindrical coordinate system 3. The spherical coordinate system
16.360 Lecture 14 Today Orthogonal coordinate systems 1.The Cartesian (rectangular) coordinate system 2.The cylindrical coordinate system 3.The spherical.
Dec 22, 2015
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
16.360 Lecture 14
• Today
Orthogonal coordinate systems
1. The Cartesian (rectangular) coordinate system2. The cylindrical coordinate system3. The spherical coordinate system
16.360 Lecture 14
• Cartesian coordinate system
x
y
z
dl
xl
yl
zl
^^^^^^
zdzydyxdxzdlydlxdlld zyx
dydzxdldlxsd zyx
^^
dxdzydldlysd zxy
^^
dxdyzdldlzsd yxz
^^
dxdydzdv
16.360 Lecture 14
• Cartesian coordinate system
x
y
z
xs
s
directions of area
16.360 Lecture 14
• Cylindrical coordinate system
z
x
y
),,( 111 zrP
^
r
^
^
z
^^^
zr ^^^
rz ^^^
rz
0^^
rr 1^^
rr
zr AzAArA^^^
222zr AAAA
1R
1
^
1
^
1 zzrrR
16.360 Lecture 14
• the differential areas and volume
^
drdzsd
^
rdzrdsd r
^
zdrrdsd z
z
x
y
dr rd
drdzrddv
16.360 Lecture 14
Example: cylindrical area
z
x
y
5
3
30
60
3/
6/
3
0
60
30
35
ddzrdS
^
rdzrdsd r
16.360 Lecture 14
• Spherical coordinate system
^^^
r^^^
R^^^
R
0^^
rr 1^^
rr
AAARA R
^^^
222 AAAA R
16.360 Lecture 14
• differential volume in Spherical coordinate system
dRRddRR
dldldlRld R
sin^^^
^^^
ddRRdldlRsd R sin2^^
dRdRdldlsd R sin^^
dRdRdldlsd R
^^
ddRdRdldRdldv sin2
16.360 Lecture 14
• Examples
(1) Find the area of the strip
60
30
360
0
2 sin ddRSdS R
(2) A sphere of radius 2cm contains a volume charge density 2cos4v
Find the total charge contained in the sphere
100/2
0
260
0
2180
0
2
100/2
0
2260
0
180
0
2
100/2
0
2260
0
180
0
))(sincos4(
))(sincos4(
)sin(
dddRR
dddRR
RdddRdvQ vv
Related Documents
