Contact formalism for dissipative mechanical systems on Lie algebroids

2023/08/02 by Simoes, Alexandre Anahory, Colombo, Leonardo, de Leon, Manuel +2 · 2 citations
#37C79 #37J37 #37J55 #53D10 #70H03 #70H05 #70H20 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2308.00990

Abstract

In this paper, we introduce a geometric description of contact Lagrangian and Hamiltonian systems on Lie algebroids in the framework of contact geometry, using the theory of prolongations. We discuss the relation between Lagrangian and Hamiltonian settings through a convenient notion of Legendre transformation. We also discuss the Hamilton-Jacobi problem in this framework and introduce the notion of a Legendrian Lie subalgebroid of a contact Lie algebroid.

Cited by

• Variational Dissipative Mechanics on Lie Algebroids
• Geometric Formulation of Combined Conservative Dissipative Mechanics via Contact Hamiltonian Dynamics Symmetries, Reduction, and Variational Integrators

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