English

Contact formalism for dissipative mechanical systems on Lie algebroids

Symplectic Geometry 2023-08-03 v1 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.2308.00990,
  title  = {Contact formalism for dissipative mechanical systems on Lie algebroids},
  author = {Alexandre Anahory Simoes and Leonardo Colombo and Manuel de Leon and Modesto Salgado and Silvia Souto},
  journal= {arXiv preprint arXiv:2308.00990},
  year   = {2023}
}

Comments

36 pages. arXiv admin note: text overlap with arXiv:2204.11537 by other authors