Symbolic Preprocessing for the Numerical Simulation of Multibody Dynamic 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. Then we use LU symbolic decomposition with Large Expression Management (LEM) to solve this leading linear system and get an explicit ODE system. Then we use the Maple command dsolve to get the numeric solution without unveiling the system, i.e. we numerically integrate the ODE system using the computation sequence, which is good for avoiding the expression explosion problem symbolically.