Lagrangian submanifolds and Hamilton-Jacobi equation
M. Barbero-Li\~n\'an, M. de Le\'on, D. Mart\'in de Diego
TL;DR
This paper explores the use of Lagrangian submanifolds to provide a geometric interpretation of the Hamilton-Jacobi equation, enabling new insights into various dynamical systems.
Contribution
It introduces a geometric framework using Lagrangian submanifolds to reinterpret the Hamilton-Jacobi equation in different dynamical contexts.
Findings
Geometric interpretation of Hamilton-Jacobi equation via Lagrangian submanifolds
Application to holonomic and nonholonomic systems
Analysis of time-dependent dynamics
Abstract
Lagrangian submanifolds are becoming a very essential tool to generalize and geometrically understand results and procedures in the area of mathematical physics. Here we use general Lagrangian submanifolds to provide a geometric version of the Hamilton-Jacobi equation. This interpretation allows us to study some interesting applications of Hamilton-Jacobi equation in holonomic, nonholonomic and time-dependent dynamics from a geometrical point of view.
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Taxonomy
TopicsControl and Dynamics of Mobile Robots · Advanced Differential Geometry Research · Advanced Differential Equations and Dynamical Systems