Variational integrators using forced discrete Hamiltonian systems

Le résumé fourni par la source

We study discrete Hamiltonian systems defined on cotangent bundles that are subjected to external forces, whose trajectories are determined by a discrete variational principle. We analyze the evolution of the canonical symplectic structure and, when a Lie group of symmetries is present, the corresponding evolution of the associated momenta. Given a continuous forced Hamiltonian system, we construct an exact discrete analogue whose order-$r$ approximations yield trajectories that approximate the continuous ones with accuracy of at least order $r$. We also give two methods to build approximate discrete systems. Combining these, we obtain a variational integrator: first approximate the exact discrete system and then solve the resulting algebraic equations of motion.

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