The Lagrange-Charpit theory of the Hamilton-Jacobi problem

DOI10.1007/s00009-021-01883-6zbMath1479.35230OpenAlexW3216803892MaRDI QIDQ2053775

Javier Pérez Alvarez

Publication date: 30 November 2021

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-021-01883-6

zbMATH Keywords

isotropic submanifoldmethod of determining a complete integral

Mathematics Subject Classification ID

Exterior differential systems (Cartan theory) (58A15) Hamilton-Jacobi equations in mechanics (70H20) Hamilton-Jacobi equations (35F21) Functional analytic methods for problems in mechanics (70G70)

Cites Work

• Hamilton-Jacobi theory, symmetries and coisotropic reduction
• Contact surgery and symplectic handlebodies
• A contact geometry framework for field theories with dissipation
• Contact Hamiltonian mechanics
• Geometric construction and properties of some families of solutions of nonlinear partial differential equations. I
• Classroom Note: The Lagrange--Charpit Method
• Systems of Hamilton-Jacobi equations
• Scalar fields and the FLRW singularity
• Liouville’s theorem and the canonical measure for nonconservative systems from contact geometry
• Cosymplectic and contact structures for time-dependent and dissipative Hamiltonian systems
• Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread
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