Geometric Hamilton-Jacobi theory for higher-order autonomous systems
Leonardo Colombo, Manuel de Le\'on, Pedro Daniel Prieto-Mart\'inez,, Narciso Rom\'an-Roy
TL;DR
This paper extends the geometric Hamilton-Jacobi theory to higher-order autonomous systems, providing a unified framework in both Lagrangian and Hamiltonian formalisms and applying it to physical examples.
Contribution
It introduces a geometric approach to Hamilton-Jacobi theory for higher-order systems, bridging Lagrangian and Hamiltonian formalisms.
Findings
Formulation of Hamilton-Jacobi equations for higher-order systems
Application to specific physical examples
Unified geometric framework for Lagrangian and Hamiltonian formalisms
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.
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