The Lagrange–Charpit Theory of the Hamilton–Jacobi Problem

Autor:	Javier Pérez Alvarez
Rok vydání:	2021
Předmět:	General Mathematics Phase space Mathematical analysis Motion (geometry) Cotangent bundle Vector field Constant (mathematics) Hamilton–Jacobi equation Manifold Mathematics Symplectic geometry
Zdroj:	Mediterranean Journal of Mathematics. 19
ISSN:	1660-5454 1660-5446
DOI:	10.1007/s00009-021-01883-6
Popis:	The Lagrange–Charpit theory is a geometric method of determining a complete integral by means of a constant of the motion of a vector field defined on a phase space associated to a nonlinear PDE of first order. In this article, we establish this theory on the symplectic structure of the cotangent bundle $$T^{*}Q$$ T ∗ Q of the configuration manifold Q. In particular, we use it to calculate explicitly isotropic submanifolds associated with a Hamilton–Jacobi equation.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::9a18f5d25f7afd9425ca6f9c24d9535f https://doi.org/10.1007/s00009-021-01883-6 Zobrazit plný text záznamu Full text from SpringerLink