Lagrangian-Hamiltonian formalism for time-dependent dissipative mechanical systems

2022/05/29 by Xavier Rivas, Daniel Torres, Rivas, Xavier +1
Physics and Astronomy · #37J55 #53D10 #53Z05 #70G45 #70H03 #70H05 #70H45 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2205.14757

openalex publication_date 2022/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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