Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems
The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the symplectic structure defined from the Lagrangian function an...
| Autores: | , , , , , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/3052 |
| Acceso en línea: | https://hdl.handle.net/2117/3052 |
| Access Level: | acceso abierto |
| Palabra clave: | Differential equations Differentiable dynamical systems Hamiltonian systems Dynamics Mechanics Lagrangian functions Hamilton–Jacobi equation Nonholonomic Lagrangian system Quasivelocity Symplectic manifold Constant of motion Complete integral Equacions diferencials ordinàries Sistemes dinàmics diferenciables Hamilton, Sistemes de Partícules (Física nuclear) Lagrange, Funcions de Classificació AMS::34 Ordinary differential equations::34A General theory Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics Classificació AMS::70 Mechanics of particles and systems::70G General models, approaches, and methods Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria |
| Sumario: | The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the symplectic structure defined from the Lagrangian function and the constraints is studied. The concept of complete solutions and their relationship with constants of motion, are also studied in detail. Local expressions using quasivelocities are provided. As an example, the nonholonomic free particle is considered. |
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