RATTLie: A variational Lie group integration scheme for constrained mechanical systems

Abstract

Variational integrators are known for their excellent numerical stability in long-term integration. In the present paper, we consider a novel second order variational integrator RATTLie for constrained systems on nonlinear configuration spaces with Lie group structure. We exploit the linear structure of the Lie algebra, which parametrizes each tangent space of the Lie group. RATTLie was inspired by the well-known RATTLE integration scheme. In order to test our method, we apply it to simulate a geometrically exact extensible Kirchhoff beam model in the form of a constrained Cosserat beam model using a nonlinear configuration space with a semi-direct product Lie group structure.