A Unified Approach to the Energy‐Consistent Numer‐ical Integration of Nonholonomic Mechanical Systems and Flexible Multibody Dynamics

The present work deals with the energy‐consistent numerical integration of mechanical systems with mixed holonomic and nonholonomic constraints. The underlying differentialalgebraic 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. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)