Research article

Lagrangian–Hamiltonian formalism for cocontact systems

  • Received: 29 May 2022 Revised: 25 July 2022 Accepted: 29 July 2022 Published: 19 October 2022
  • Primary: 37J55; Secondary: 70H03, 70H05, 53D10, 70G45, 53Z05, 70H45

  • 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.

    Citation: Xavier Rivas, Daniel Torres. Lagrangian–Hamiltonian formalism for cocontact systems[J]. Journal of Geometric Mechanics, 2023, 15(1): 1-26. doi: 10.3934/jgm.2023001

    Related Papers:

  • 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.



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