A symmetric splitting method for rigid body dynamics

It has been known since the time of Jacobi that the solution to the free rigid body Euler equations of motion is given in terms of a certain type of elliptic functions. Using the Arithmetic-Geometric mean algorithm, Abramowitz & Stegun (1992), these functions can be calculated efficiently and accurately. The overall approach yields a faster and more accurate numerical solution to the Euler equations compared to standard numerical ODE and symplectic solvers. In this paper we investigate the possibility of extending this approach to the case of rigid bodies subject to external forces. By using a splitting strategy similar to the one proposed in Reich (1996), we decompose the vector field of our problem in a free rigid body (FRB) problem and another completely integrable vector held. We apply the method to the simulation of the heavy top.