New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries

We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented Lagrangian formalisms, studying their equivalence. We define several kinds o...

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Bibliographic Details
Published inInternational journal of geometric methods in modern physics Vol. 17; no. 6; p. 2050090
Main Authors Gaset, Jordi, Gràcia, Xavier, Muñoz-Lecanda, Miguel C., Rivas, Xavier, Román-Roy, Narciso
Format Journal Article
LanguageEnglish
Published Singapore World Scientific Publishing Company 01.05.2020
World Scientific Publishing Co. Pte., Ltd
Subjects
Formalism
Mechanical systems
Research Article
Lagrangian formalism
dissipation law
Contact manifold
symmetry
dissipative system
Hamiltonian formalism
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ISSN0219-8878
1793-6977
1793-6977
DOI10.1142/S0219887820500905

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Summary:We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented Lagrangian formalisms, studying their equivalence. We define several kinds of symmetries for contact dynamical systems, as well as the notion of dissipation laws, prove a dissipation theorem and give a way to construct conserved quantities. Some well-known examples of dissipative systems are discussed.
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ISSN:0219-8878
1793-6977
1793-6977
DOI:10.1142/S0219887820500905