EQUIVARIANT CONSTRAINED SYMPLECTIC INTEGRATION

We use recent results an symplectic integration of Hamiltonian systems with constraints to construct symplectic integrators on cotangent bun dles of manifolds by embedding the manifold in a linear space. We also prove that these methods are equivariant under cotangent lifts of a s ymmetry group acting linearly on the ambient space and consequently pr eserve the corresponding momentum. These results provide an elementary construction of symplectic integrators for Lie-Poisson systems and ot her Hamiltonian systems with symmetry. The methods are illustrated on the free rigid body, the heavy top, and the double spherical pendulum.