E. Barth and B. Leimkuhler

Besides preserving the energy, the flow of a conservative multibody system possesses important geometric ( symplectic) invariants. Symplectic discretization schemes that mimic the corresponding feature of the true flow have been shown to be effective alternatives to standard methods for many conservative problems. For systems of rigid bodies, the development of such schemes can be complicated or costly to implement, depending on the choice of problem formulation. In this article, we demonstrate that a special formulation of the multibody system (based on a particle representation) together with a symplectic discretization for constrained problems borrowed from molecular dynamics offers an efficient alternative to standard approaches. Numerical experiments illustrating the new approach are described.