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Singular Lagrangians and precontact Hamiltonian Systems

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arxiv 1904.11429 v1 pith:U5PEDQXJ submitted 2019-04-25 math-ph math.MPmath.SG

Manuel de León , Manuel Lainz Valcázar This is my paper · ORCID
classification math-phmath.MPmath.SG
keywords systemsalgorithmbrackethamiltonianlagrangiansimilarsingularbehavior
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In this paper we discuss singular Lagrangian systems on the framework of contact geometry. These systems exhibit a dissipative behavior in contrast with the symplectic scenario. We develop a constraint algorithm similar to the presymplectic one studied by Gotay and Nester (the geometrization of the well-known Dirac-Bergman algorithm). We also construct the Hamiltonian counterpart and prove the equivalence with the Lagrangian side. A Dirac-Jacobi bracket is constructed similar to the Dirac bracket.

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  1. Numerical integration in celestial mechanics: a case for contact geometry

    math.NA 2019-09 conditional novelty 6.0 of 10

    All linearly damped Newton equations of a certain broad class are shown to fit a contact-geometry framework, which yields new higher-order geometric integrators with derived error estimates, tested on Kepler, spin-orb...

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