Collective Symplectic Integrators on $S_2^N \times T^*\mathbb{R}^M$

Abstract

A novel symplectic integrator for Hamiltonian equations on $S_2^n \times T^{\ast} \RR^m$ is developed and studied. Partitioned Runge--Kutta methods for Hamiltonian systems on products of Hamiltionian manifolds are studied, specifically, algebraic conditions for their symplecticity are derived.