Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Caruso, M. I., Fernandez, J., Tori, C. I., Zuccalli, M.
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167640487
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