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<p>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.</p>

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Contact formalism for dissipative mechanical systems on Lie algebroids

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月25日

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  • Alexandre Anahory Simoes,
  • Leonardo Colombo,
  • Manuel de León,
  • Modesto Salgado,
  • Silvia Souto

摘要

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.