Discrete Hamilton–Jacobi theory for systems with external forces

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 char...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2022-05, Vol.55 (20), p.205201
Main Authors: de León, Manuel, Lainz, Manuel, López-Gordón, Asier
Format: Article
Language:English
Subjects:
discrete mechanics
friction
geometric mechanics
Hamilton–Jacobi theory
Rayleigh dissipation
variational integrators
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Summary: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.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ac6240