Many-body systems: graph-theoretic approach

  • Peter W. Likins
  • Robert E. Roberson
  • Jens Wittenburg
Part of the International Centre for Mechanical Sciences book series (CISM, volume 103)


In the previous lecture the system was described for which now a dynamical formalism is to be developed. The system was said to consist of an arbitrary number of rigid bodies. It has a topological tree-structure. Its hinges of one, two or three degrees of freedom of relative rotational motion contain at least one point which is a fixed point on either one of the two bodies connected by the respective hinge. This point was called the hinge point. A tree-structure of n bodies has n−1 hinge points. The dynamical formalism to be developed must combine the following advantages:
  1. a)

    it must be exact, i.e. no approximations are accepted

  2. b)

    it must lead to equations the various terms of which are simple to interprete physically

  3. c)

    it must be easily applicable to mechanical problems of different nature

  4. d)

    it must be formulated in such a way that it can be easily put on a digital computer



Incidence Matrix Column Matrix Graph Theoretical Approach Hinge Point Vertex Number 
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Copyright information

© Springer-Verlag Wien 1971

Authors and Affiliations

  • Peter W. Likins
    • 1
  • Robert E. Roberson
    • 1
  • Jens Wittenburg
    • 2
  1. 1.University of CaliforniaUSA
  2. 2.University of HannoverGermany

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