Abstract
The process of determining the potential energy, as a function of generalized coordinates, of a system consisting of rigid bodies and springs is often extremely laborious. In this paper, a method is presented by means of which all the potential energy terms of a system are calculated in a systematic manner. It is assumed that the system of rigid bodies has a topological tree structure, and that linear springs are situated arbitrarily between the rigid bodies. The method is based on a graph-theoretical approach and is consistent with that of the calculation of kinetic energy presented in ( 2 , J. Franklin Inst., Vol. 324, No. 3, pp. 351–367, 1987). The paper contains the derivation of general formulae for potential energies of gravity and elastic forces. These formulae are implemented for the case of a planar system; an example is also provided.
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