Infinitesimal symmetries in Contact Hamiltonian systems

Abstract

In this paper, we extend the well-known Noether theorem for Lagrangian systems to contact Lagrangian systems. We introduce a classification of infinitesimal symmetries and obtain the corresponding dissipated quantities. We notice that in contact dynamics, the existence of infinitesimal symmetries does not produce conserved quantities, but functions that dissipate at the same rate than the energy; so, the corresponding quotients are true conserved quantities.

References in corpus (5)

• Singular Lagrangians and precontact Hamiltonian Systems
• Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on $S^2\times S^3$
• Contact flows and integrable systems
• Scalar Fields and the FLRW Singularity
• Noether symmetries and integrability in time-dependent Hamiltonian mechanics

Cited by in corpus (13)

• New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries
• Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread
• On the geometry of discrete contact mechanics
• Unified Lagrangian-Hamiltonian formalism for contact systems
• Symmetries, conservation and dissipation in time-dependent contact systems
• Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems
• Contact Lie systems
• Application of Herglotz's Variational Principle to Electromagnetic Systems with Dissipation
• The Herglotz variational principle for dissipative field theories
• Lie integrability by quadratures for symplectic, cosymplectic, contact and cocontact Hamiltonian systems
• Constrained Lagrangian dissipative contact dynamics
• Contact line bundles, foliations, and integrability
• Relative Equilibria for Scaling Symmetries and Central Configurations