The Lie-Trotter integrator in the dynamics of the symmetric free rigid body
This is an incremental theoretical result for researchers working on geometric numerical integration of rigid body dynamics.
The paper shows that the Lie-Trotter integrator, when applied to Euler equations for the symmetric free rigid body, is a Poisson integrator. No concrete numerical results are provided.
The numerical integration plays a fundamental role in understanding the behaviour of many mechanical systems. In this paper some important aspects of the mechanical integrators on the dynamics of a mechanical system are studied. More specific, we have shown that if that the Lie-Trotter integrator is obtained, in case of Euler equations for the dynamics of symmetric free rigid body, then it is a Poisson integrator. At the end of the paper some important remarks are presented.