Geometric Hamilton-Jacobi theory for systems with external forces

Abstract

In this paper, we develop a Hamilton-Jacobi theory for forced Hamiltonian and Lagrangian systems. We study the complete solutions, particularize for Rayleigh systems and present some examples. Additionally, we present a method for the reduction and reconstruction of the Hamilton-Jacobi problem for forced Hamiltonian systems with symmetry. Furthermore, we consider the reduction of the Hamilton-Jacobi problem for a Čaplygin system to the Hamilton-Jacobi problem for a forced Lagrangian system.

39 pages, submitted to J. Math. Phys

References in corpus (9)

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Cited by in corpus (5)

• Reviewing the Geometric Hamilton-Jacobi Theory concerning Jacobi and Leibniz identities
• Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems
• Discrete Hamilton-Jacobi theory for systems with external forces
• Hamilton-Jacobi theory for nonholonomic and forced hybrid mechanical systems
• Generalized hybrid momentum maps and reduction by symmetries of forced mechanical systems with inelastic collisions