Well posed formulations of holonomic mechanical system dynamics and design sensitivity analysis

Abstract

Manifold theoretic ordinary differential equations of motion for holonomic mechanical systems that depend on problem data, or design variables, are shown to be well posed; i.e., they have a unique solution that depends continuously on problem data. It is proved that these differential equations are equivalent to the d’Alembert variational formulation and the index 3 Lagrange multiplier formulation of differential-algebraic equations of motion, which are also shown to be well posed. These results provide a foundation for dynamic system design sensitivity analysis, which requires differentiability of solutions of the equations of motion with respect to design variables.