Momentum conserving symplectic integrators (Q1344789)

It is shown that symplectic partitioned Runge-Kutta methods conserve momentum maps corresponding to linear symmetry groups acting on the phase space of Hamiltonian differential equations by extended point transformation. This result is generalized to constrained systems, and the author shows how this conservation property relates to the symplectic integration of Lie-Poisson systems on certain submanifolds of the general matrix group.