Contact Lagrangian systems subject to impulsive constraints

Abstract

We describe geometrically contact Lagrangian systems under impulsive forces and constraints, as well as instantaneous nonholonomic constraints which are not uniform along the configuration space. In both situations, the vector field describing the dynamics of a contact Lagrangian system is determined by defining projectors to evaluate the constraints by using a Riemannian metric. In particular, we introduce the Herglotz equations for contact Lagrangian systems subject to instantaneous nonholonomic constraints. Moreover, we provide a Carnot-type theorem for contact Lagrangian systems subject to impulsive forces and constraints, which characterizes the changes of energy due to contact-type dissipation and impulsive forces. We illustrate the applicability of the method with practical examples, in particular, a rolling cylinder on a springily surface and a rolling sphere on a non-uniform surface, both with dissipation.

arXiv comment23 pages

References in corpus (12)

• Contact Hamiltonian Mechanics
• 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
• From Lagrangian mechanics to nonequilibrium thermodynamics: a variational perspective
• A contact geometry framework for field theories with dissipation
• Singular Lagrangians and precontact Hamiltonian Systems
• A $k$-contact Lagrangian formulation for nonconservative field theories
• Mechanical systems subjected to generalized nonholonomic constraints
• A review on contact Hamiltonian and Lagrangian systems
• Nonsmooth Herglotz variational principle
• Geometrical aspects of contact mechanical systems and field theories

Cited by in corpus (3)

• Nonsmooth Herglotz variational principle
• Generalized virial theorem for contact Hamiltonian systems
• On the integrability of hybrid Hamiltonian systems