Application of graph theory to the determination of potential energy of systems consisting of rigid bodies and springs
This paper follows a previous study of the author [ibid. 324, 351-367 (1987; Zbl 0643.70002)] on the application of graph theory to the determination of kinetic energy of rigid body systems. The potential energy of a system consisting of rigid bodies is calculated in a systematic manner using a graph theoretical method. The notations are those of \textit{J. Wittenburg} [Dynamics of systems of rigid bodies (1977; Zbl 0363.70004)] and it is assumed that the system has a topological tree structure. Two kinds of problems are considered: the potential energy of gravity forces and the potential energy of springs. The main aim of this paper is the calculation of the potential energy of a system of rigid bodies connected by a system of simple linear translational springs. In this case, two graphs are needed at the same time, one displays the interconnection structure of the system of solids by the hinges, the other displays the topological structure of the system of linear springs. The general formula for the potential energy is derived. Implementation is performed in the case of planar systems and an example is provided.
scientific article; zbMATH DE number 4078867