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arXiv · 2110.14431

Discrete Hamilton-Jacobi theory for systems with external forces

Manuel de León·Manuel Lainz·Asier López-Gordón
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Abstract

This paper is devoted to discrete mechanical systems subject to external forces. We introduce a discrete version of systems with Rayleigh-type forces, obtain the equations of motion and characterize the equivalence for these systems. Additionally, we obtain a Noether's theorem and other theorem characterizing the Lie subalgebra of symmetries of a forced discrete Lagrangian system. Moreover, we develop a Hamilton-Jacobi theory for forced discrete Hamiltonian systems. These results are useful for the construction of so-called variational integrators, which, as we illustrate with some examples, are remarkably superior to the usual numerical integrators such as the Runge-Kutta method.

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BibTeXRIS

Manuel de León, Manuel Lainz, Asier López-Gordón. 2021-10-27. Discrete Hamilton-Jacobi theory for systems with external forces. https://doi.org/10.1088/1751-8121%2Fac6240

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