Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems

Abstract

In this paper, we study the integrability of contact Hamiltonian systems, both time-dependent and independent. In order to do so, we construct a Hamilton--Jacobi theory for these systems following two approaches, obtaining two different Hamilton--Jacobi equations. Compared to conservative Hamiltonian systems, contact Hamiltonian systems depend of one additional parameter. The fact of obtaining two equations reflects whether we are looking for solutions depending on this additional parameter or not. In order to illustrate the theory developed in this paper, we study three examples: the free particle with a linear external force, the freely falling particle with linear dissipation and the damped and forced harmonic oscillator.

27 pages

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Cited by in corpus (7)

• Multicontact formulation for non-conservative field theories
• Symmetries, conservation and dissipation in time-dependent contact systems
• Nonautonomous k-contact field theories
• The Herglotz variational principle for dissipative field theories
• A review on coisotropic reduction in Symplectic, Cosymplectic, Contact and Co-contact Hamiltonian systems
• Practical Introduction to Action-Dependent Field Theories
• Liouville-Arnold theorem for homogeneous symplectic and contact Hamiltonian systems