Energy-consistent numerical integration of mechanical systems with mixed holonomic and nonholonomic constraints

Abstract

The present work deals with the energy-consistent numerical integration of mechanical systems with mixed holonomic and nonholonomic constraints. The underlying differential-algebraic equations (DAEs) with index three are directly discretized. This approach makes possible the development of a new energy-consistent time-stepping scheme for general nonholonomic systems. In particular, both nonholonomic problems from rigid body dynamics as well as flexible multibody dynamics can be treated in a unified manner. In this connection specific constrained formulations of rigid bodies and geometrically exact beams are presented. Moreover, the newly developed discrete null space method is applied to achieve a size-reduction and an improved conditioning of the discrete system. The numerical examples deal with a nonholonomic rigid body system and a flexible multibody system.