Contact Hamiltonian and Lagrangian systems with nonholonomic constraints

León Manuel de; Jiménez Víctor M.; Lainz Manuel

doi:10.3934/jgm.2021001

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2021, Volume 13, Issue 1: 25-53. Doi: 10.3934/jgm.2021001

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Contact Hamiltonian and Lagrangian systems with nonholonomic constraints

1.
Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), C\Nicolás Cabrera, 13-15, Campus Cantoblanco, UAM, 28049 Madrid, Spain
2.
Universidad de Alcalá (UAH) Campus Universitario. Ctra. Madrid-Barcelona, Km. 33, 600. 28805 Alcal´a de Henares, Madrid, Spain
3.
Real Academia de Ciencias Exactas, Fisicas y Naturales C/de Valverde 22, 28004 Madrid, Spain

Dedicated to Professor Tony Bloch on the occasion of his 65th birthday

Received: October 31, 2019

Revised: September 30, 2020

Published: March 2021

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Abstract

In this article we develop a theory of contact systems with nonholonomic constraints. We obtain the dynamics from Herglotz's variational principle, by restricting the variations so that they satisfy the nonholonomic constraints. We prove that the nonholonomic dynamics can be obtained as a projection of the unconstrained Hamiltonian vector field. Finally, we construct the nonholonomic bracket, which is an almost Jacobi bracket on the space of observables and provides the nonholonomic dynamics.

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Mathematics Subject Classification: 37J60;70F25;53D10;70H33.

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