Symbolic Computation Sequences and Numerical Analytic Geometry Applied to Multibody Dynamical Systems

The symbolic-numeric computing described here consists of an extensive symbolic pre-processing of systems of differential-algebraic equations (DAE), followed by the numerical integration of the system obtained. The application area is multibody dynamics. We deal symbolically with a DAE system using differentiation and elimination methods to find all the hidden constraints, and produce a system that is leading linear (linear in its leading derivatives). Then we use LU symbolic decomposition with Large Expression Management to solve this leading linear system for its leading derivatives, thereby obtaining an explicit ODE system written in terms of computation sequences obtained from using theMaple package LargeExpressions. Subsequently the Maple command dsolve is applied to this explicit ODE to obtain its numeric solution. Advantages of this strategy in avoiding expression explosion are illustrated and discussed. We briefly discuss a new class of methods involving Numerical Algebraic and Analytic Geometry. Mathematics Subject Classification (2000). Primary 70E55; Secondary 68U01; Tertiary 15A09.