GRAPH THEORETICAL APPROACH .2. DETERMINATION OF GENERALIZED FORCES FOR A CLASS OF SYSTEMS CONSISTING OF PARTICLES AND SPRINGS

The process of determining the generalized forces (as a function of generalized coordinates and system parameters) of a system consisting of mass particles and springs is often extremely laborious. In this paper, a method is presented where the derived formulae have a form of evident functions not only of generalized coordinates and system parameters but also of the topological structure of a system. This paper contains the derivation of general formulae for potential energies of gravity and elastic forces as well as for the generalized forces related to both potential and nonpotential forces acting on a system of particles. It is assumed that the system of particles has a topological tree structure, and that linear springs are situated arbitrarily between the particles. The method is based on a graph-theoretical approach and is consistent with the kinetic energy calculation presented in Arczewski (J. Franklin Inst., Vol. 329, pp. 469-481, 1992).