Lie group vs. classical time integrators in multibody dynamics: Formulations and numerical benchmarks

The dynamics of flexible multibody systems with large rotations is often described using large sets of index-3 differential-algebraic equations. In this context, the Lie group structure of the dynamic system may be exploited in order to provide an elegant solution to the rotation parameterization problem.
The talk discusses an original Lie-group extension of the classical generalized-alpha method, which can be used to solve index-3 differential-algebraic equations in multibody dynamics. Second-order accuracy is demonstrated at least in the unconstrained case and the performance is illustrated on several critical benchmarks with high rotational speeds. The remarkable simplicity of the new algorithms opens some interesting perspectives for real-time applications, model-based control and optimization of multibody systems.