Summary
We use recent results on symplectic integration of Hamiltonian systems with constraints to construct symplectic integrators on cotangent bundles of manifolds by embedding the manifold in a linear space. We also prove that these methods are equivariant under cotangent lifts of a symmetry group acting linearly on the ambient space and consequently preserve the corresponding momentum. These results provide an elementary construction of symplectic integrators for Lie-Poisson systems and other Hamiltonian systems with symmetry. The methods are illustrated on the free rigid body, the heavy top, and the double spherical pendulum.
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Communicated by Jerrold Marsden
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McLachlan, R.I., Scovel, C. Equivariant constrained symplectic integration. J Nonlinear Sci 5, 233–256 (1995). https://doi.org/10.1007/BF01212956
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DOI: https://doi.org/10.1007/BF01212956