Symbolic computer language for multibody systems

Abstract

Methods are developed for describing and manipulating symbolic data "objects" that are useful for analyzing the kinematics and dynamics of multibody systems. These symbolic objects include: (1) vector/dyadic algebraic expressions, (2) physical components in a multibody system, and (3) program structures needed in a numerical simulation code. A computer algebra language based on these methods encourages the automation of multibody analyses that are versatile and simple, because much of the "work" involved in describing the system mathematically is handled by the algebra system, rather than the analysis formalism. It also handles much of the process of converting symbolic equations into efficient computer code for numerical analysis. The language permits a dynamicist to describe forces, moments, constraints, and output variables using expressions involving arbitrary combinations of unit-vectors from different moving reference frames. Kinematics and dynamics analysis algorithms have been programmed that employ these capabilities to analyze complex multibody systems and formulate highly efficient computer source code used for subsequent numerical analysis. A companion paper describes the basic multibody formalism that has been programmed.