On the geometry of discrete contact mechanics

Abstract

In this paper, we continue the construction of variational integrators adapted to contact geometry started in \cite{VBS}, in particular, we introduce a discrete Herglotz Principle and the corresponding discrete Herglotz Equations for a discrete Lagrangian in the contact setting. This allows us to develop convenient numerical integrators for contact Lagrangian systems that are conformally contact by construction. The existence of an exact Lagrangian function is also discussed.

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• Contact Hamiltonian Systems
• New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries
• Contact manifolds and dissipation, classical and quantum
• Infinitesimal symmetries in Contact Hamiltonian systems
• Singular Lagrangians and precontact Hamiltonian Systems
• Contact variational integrators
• Secular resonance sweeping and orbital excitation in decaying disks
• Morse families and Dirac systems

Cited by in corpus (2)

• The flow method for the Baker-Campbell-Hausdorff formula: exact results
• Geometric numerical integration of Liénard systems via a contact Hamiltonian approach