Applications of Symbolic Computing for Numerical Analysis of Mechanical Systems

The symbolic computing system MACSYMA is used to automatically generate the explicit equations necessary to represent the kinematic constraints and system dynamics and to compute the design sensitivities for optimal design of any multibody system. The logic to construct system matrices and vectors involved in the analysis and design equations is implemented as general purpose MACSYMA programs. All necessary manipulations are performed by MACSYMA and the equations are output as FORTRAN statements that can be compiled and executed. This approach results in a computational saving of up to 95% compared to using a general purpose programs. The approach is general in nature and is applicable to any multibody system. Examples are presented to demonstrate the effectiveness of the approach.