Computer-Assisted Generation of Dynamical Equations for Multibody Systems

Abstract

A computer-oriented method based on Kane's equations is presented that facilitates the formulation of dynamical equa tions. The method requires an analyst to formulate only the most basic ingredients of the equations in analytical form; the necessary summations and multiplications required for the final equations are left to a small computer program. Examples are shown of two short programs, which either per form the necessary numerical operations or generate equa tions in symbolic form. As for the requisite kinematical anal ysis, only velocities and angular velocities are needed, and no accelerations or kinetic energies must be formed. The method systematically avoids unnecessary operations such as the introduction and subsequent elimination of nonworking contact forces, the computation of velocity dependent terms that ultimately cancel one another, and the calculation of expressions that are determined by symmetry properties of matrices.