Comparison of Geometric Integrators for Rigid Body Simulation

Geometric integrators are numerical timestepping schemes which preserve invariant structures associated to physical dynamical systems. For example, a symplectic integrator is one which preserves a strong differential invariant of the flows of Hamiltonian systems (the 2-form dq ^dp associated to canonical variables q,p). For constrained systems such as the rigid body, preservation of geometric phase-flow structure is complicated by the choice of coordinates and the need for efficiency. Nowhere are these issues more critical than in the simulation of rigid body systems. In recent work, several alternative geometric approaches to rigid body systems integrators have been proposed and applied in molecular simulation. In this article, these methods are introduced and compared with a simple model problem.