Geometric Hamilton-Jacobi theory for higher-order autonomous systems

Abstract

The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi equations in these formalisms and apply our results to analyze some particular physical examples.

26 pp. Revised version: Minor corrections done. References updated

References in corpus (4)

• Hamilton-Jacobi Theory in k-Symplectic Field Theories
• Hamilton-Jacobi theory in k-cosymplectic field theories
• The Hamilton-Jacobi Formalism for Higher Order Field Theories
• Hamilton-Jacobi Diffieties

Cited by in corpus (12)

• Higher order mechanics on graded bundles
• On the role of geometry in statistical mechanics and thermodynamics I: Geometric perspective
• Reviewing the Geometric Hamilton-Jacobi Theory concerning Jacobi and Leibniz identities
• Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems
• Tulczyjew Triples in Higher Derivative Field Theory
• Structural aspects of Hamilton-Jacobi theory
• Geometric Hamilton-Jacobi theory for systems with external forces
• A Hamilton-Jacobi formalism for higher order implicit systems
• Hamilton-Jacobi theory in multisymplectic classical field theories
• Unified formalism for the generalized kth-order Hamilton-Jacobi problem
• Hamilton-Jacobi theory for gauge field theories
• An overview of the Hamilton--Jacobi theory: the classical and geometrical approaches and some extensions and applications