Lagrangian–Hamiltonian formalism for cocontact systems-Reference-Cited by-同舟云学术

Lagrangian–Hamiltonian formalism for cocontact systems

Published:2023 Issue:1 Volume:15 Page:1-26
ISSN:1941-4889
Container-title:Journal of Geometric Mechanics
language:
Short-container-title:JGM

Author:

Rivas Xavier¹,Torres Daniel²

Affiliation:

1. Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Logroño, Spain

2. Universitat Politècnica de Catalunya, Barcelona, Spain

Abstract

<abstract><p>In this paper we present a unified Lagrangian–Hamiltonian geometric formalism to describe time-dependent contact mechanical systems, based on the one first introduced by K. Kamimura and later formalized by R. Skinner and R. Rusk. This formalism is especially interesting when dealing with systems described by singular Lagrangians, since the second-order condition is recovered from the constraint algorithm. In order to illustrate this formulation, some relevant examples are described in full detail: the Duffing equation, an ascending particle with time-dependent mass and quadratic drag, and a charged particle in a stationary electric field with a time-dependent constraint.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Control and Optimization,Geometry and Topology,Mechanics of Materials

Reference49 articles.

1. R. Skinner, R. Rusk, Generalized Hamiltonian dynamics I: Formulation on $ \mathrm{T}^\ast Q\oplus \mathrm{T} Q$, J. Math. Phys., 24 (1983), 2589–2594. https://doi.org/10.1063/1.525654

2. K. Kamimura, Singular Lagrangian and constrained Hamiltonian systems, generalized canonical formalism, Nuovo Cim. B, 68 (1982), 33–54. https://doi.org/10.1007%2FBF02888859

3. M. Barbero-Liñán, A. Echeverría-Enríquez, D. Martín de Diego, M. C. Muñoz-Lecanda, N. Román-Roy, Unified formalism for non-autonomous mechanical systems, J. Math. Phys., 49 (2008), 062902. https://doi.org/10.1063/1.2929668

4. J. Cortés, S. Martínez, F. Cantrijn, Skinner–Rusk approach to time-dependent mechanics, Phys. Lett., 300 (2002), 250–258. https://doi.org/10.1016/S0375-9601(02)00777-6

5. X. Gràcia, R. Martín, Geometric aspects of time-dependent singular differential equations, Int. J. Geom. Methods Mod. Phys., 2 (2005), 597–618. https://doi.org/10.1142/S0219887805000697

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