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Mathematical Modeling of Physical Systems
Multi-bond Graphs
• We shall today look at vectors of bonds, calledl i b dmulti-bonds.
• Especially when dealing with 2D and 3Dmechanics, the d’Alembert principle must beapplied to each degree of freedom separately.
• Each equation looks structurally the same.• This leads naturally to a demand for multi-bondThis leads naturally to a demand for multi bond
AnalysisIt has been possible to describe the motion of the planarpendulum by a bond graph enhanced by activated bonds forthe description of the holonomic constraint. Unfortunately,the bond graph doesn’t tell us much that we didn’t knowalready
We shouldn’t have to derive the equations first in order to be able
already.
to derive the bond graph from them.
The resulting bond graph didn’t preserve the topological properties The resulting bond graph didn t preserve the topological properties of the system in any recognizable form.
Multi-bond Graph Basics• The basic multi-bond graph models contain little that is
surprising They represent essentially natural extensions ofsurprising. They represent essentially natural extensions ofthe regular bond graph models.
• A few points are worth mentioning though. First, there isp g g ,the defaults model that must be included in each multi-bond graph model. It contains only a single parameter, thedimensional parameter, n, that specifies, how many bondseach multi-bond contains by default.Th d f lt d l t b f d i h lti b d• The defaults model must be referenced in each multi-bondgraph model as an outer model.
Multi-bond Graph Basics III• A second difference concerns the use of junctions.
Whereas the general bond graph library provides separateWhereas the general bond graph library provides separatejunction models for 2..6 bond connections, the multi-bondgraph library offers only junctions with either 4 or 8connectors. Yet, individual connectors may be leftunconnected as needed.
• A third difference is in the use of transformers andgyrators. The multi-bond graph library offers a muchlarger variety of different transformer and gyrator modelslarger variety of different transformer and gyrator modelswhen compared to the regular bond graph library.
• Finally, although the library offers causal multi-bonds, these are much less useful than the causalregular bonds, because many multi-bonds havemixed computational causality. Hence causalmulti-bonds are rarely used in practice.
• Zimmer D (2006) A Modelica Library forZimmer, D. (2006), A Modelica Library forMultiBond Graphs and its Application in 3D-Mechanics, MS Thesis, Dept. of ComputerMechanics, MS Thesis, Dept. of ComputerScience, ETH Zurich.
i d C lli (2006) “ h• Zimmer, D. and F.E. Cellier (2006), “TheModelica Multi-bond Graph Library,” Proc. 5th
• Cellier, F.E. and D. Zimmer (2006), “WrappingM l i b d G h A S d A hMulti-bond Graphs: A Structured Approach toModeling Complex Multi-body Dynamics,”Proc 20th European Conference on ModelingProc. 20th European Conference on Modelingand Simulation, Bonn, Germany, pp. 7-13.