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arXiv · 2607.02694

Variational integrators using forced discrete Hamiltonian systems

M. I. Caruso·J. Fernandez·C. I. Tori·M. Zuccalli
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Abstract

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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M. I. Caruso, J. Fernandez, C. I. Tori, M. Zuccalli. 2026-07-02. Variational integrators using forced discrete Hamiltonian systems. https://arxiv.org/abs/2607.02694

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