Unified Lagrangian‐Hamiltonian Formalism for Contact Systems

León, Manuel de; Gaset, Jordi; Valcázar, Manuel Lainz; Rivas, Xavier; Román‐Roy, Narciso

doi:10.1002/prop.202000045

Cited by 18 publications

(18 citation statements)

References 43 publications

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“…In [25], the authors develop a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of contact autonomous mechanical systems, which is based on the approach of the pioneering work of R. Skinner and R. Rusk [69]. This framework permits to skip the second order differential equation problem, which is obtained as a part of the constraint algorithm (for singular or regular Lagrangians), and is specially useful to describe singular Lagrangian systems.…”

Section: • Uniform Formalismmentioning

confidence: 99%

A review on contact Hamiltonian and Lagrangian systems

León¹,

Laínz²

2020

Preprint

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Contact Hamiltonian dynamics is a subject that has still a short history, but with relevant applications in many areas: thermodynamics, cosmology, control theory, and neurogeometry, among others. In recent years there has been a great effort to study this type of dynamics both in theoretical aspects and in its potential applications in geometric mechanics and mathematical physics. This paper is intended to be a review of some of the results that the authors and their collaborators have recently obtained on the subject.

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Section: • Uniform Formalismmentioning

confidence: 99%

A review on contact Hamiltonian and Lagrangian systems

León¹,

Laínz²

2020

Preprint

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“…This is recently studied in [54]. Another way is to generalize the unified formalism for contact dynamics as presented in a recent study [55]. In this paper, our interest is to study the Legendre transformation for contact dynamics following the understanding of Tulczyjew.…”

Section: Introductionmentioning

confidence: 99%

Contact Dynamics: Legendrian and Lagrangian Submanifolds

et al. 2021

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We are proposing Tulczyjew’s triple for contact dynamics. The most important ingredients of the triple, namely symplectic diffeomorphisms, special symplectic manifolds, and Morse families, are generalized to the contact framework. These geometries permit us to determine so-called generating family (obtained by merging a special contact manifold and a Morse family) for a Legendrian submanifold. Contact Hamiltonian and Lagrangian Dynamics are recast as Legendrian submanifolds of the tangent contact manifold. In this picture, the Legendre transformation is determined to be a passage between two different generators of the same Legendrian submanifold. A variant of contact Tulczyjew’s triple is constructed for evolution contact dynamics.

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“…More recently, the study of the geometrization of dissipative systems [10,27,46], in its natural framework of contact geometry [3,32,39], has gained momentum, although the Lagrangian version was available since the 1930s thanks to the developments of Gustav Herglotz [37,38]. Contact mechanics [6,8,9,12,16,17,17,19,28,41] is also the natural framework for studying thermodynamics as early as Constantin Carathéodory (the first quarter of the past century), although its applications today cover many other fields [7,12,29,30,35,39,48,49].…”

Section: Introductionmentioning

confidence: 99%

Constrained Lagrangian dissipative contact dynamics

de León,

Laínz,

Muñoz-Lecanda

et al. 2021

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We show that the contact dynamics obtained from the Herglotz variational principle can be described as a constrained nonholonomic or vakonomic ordinary Lagrangian system depending on a dissipative variable with an adequate choice of one constraint. As a consequence we obtain the dynamics of contact nonholonomic and vakonomic systems as ordinary variational calculus with constraints on a Lagrangian with a dissipative variable. The variation of the energy and the other dissipative quantities are also obtained giving the usual results.

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Unified Lagrangian‐Hamiltonian Formalism for Contact Systems

Cited by 18 publications

References 43 publications

A review on contact Hamiltonian and Lagrangian systems

A review on contact Hamiltonian and Lagrangian systems

Contact Dynamics: Legendrian and Lagrangian Submanifolds

Constrained Lagrangian dissipative contact dynamics

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