A unified framework for mechanics. Hamilton-Jacobi equation and applications

Abstract

In this paper, we construct Hamilton-Jacobi equations for a great variety of mechanical systems (nonholonomic systems subjected to linear or affine constraints, dissipative systems subjected to external forces, time-dependent mechanical systems...). We recover all these, in principle, different cases using a unified framework based on skew-symmetric algebroids with a distinguished 1-cocycle. Several examples illustrate the theory.

30 pages, 3 figures

References in corpus (3)

• Geometric Hamilton-Jacobi Theory for Nonholonomic Dynamical Systems
• Nonholonomic Hamilton-Jacobi equation and Integrability
• A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids

Cited by in corpus (13)

• Geometric Hamilton-Jacobi theory for higher-order autonomous systems
• Reviewing the Geometric Hamilton-Jacobi Theory concerning Jacobi and Leibniz identities
• A Hamilton-Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds
• Extended Hamilton-Jacobi theory, contact manifolds and integrability by quadratures
• One invariant measure and different Poisson brackets for two nonholonomic systems
• Structural aspects of Hamilton-Jacobi theory
• Hamilton-Jacobi theory in multisymplectic classical field theories
• A Hamilton-Jacobi formalism for higher order implicit systems
• A new perspective on nonholonomic brackets and Hamilton-Jacobi theory
• Hamilton-Jacobi theory for gauge field theories
• An overview of the Hamilton--Jacobi theory: the classical and geometrical approaches and some extensions and applications
• Reduction of hybrid Hamiltonian systems with non-equivariant momentum maps
• Homogeneous bi-Hamiltonian structures and integrable contact systems