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Graph theoretical approach—II. determination of generalized forces for a class of systems consisting of particles and springs

✍ Scribed by Krzysztof Arczewski

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
460 KB
Volume
329
Category
Article
ISSN
0016-0032

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✦ Synopsis

The process of determining the generalized ji)rces (as a finction /?f'generalized coordinates and s,vstem parameters) qf 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 f&n 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 ofgeneral jbrmulae ,for potential energies of'grarity and elastic ,fi)rces as we/L as ,for the generalized ,fi)rces related to both potential and nonpotential.forces acting on a system of particles. It is assumed that the sIxtern of particles has a topolqical 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.

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