Unified formalism for non-autonomous mechanical systems
We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency ar...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2008 |
| 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:2117/1926 |
| Acceso en línea: | https://hdl.handle.net/2117/1926 |
| Access Level: | acceso abierto |
| Palabra clave: | Lagrangian functions Symplectic manifolds Hamiltonian systems Lagrangian and Hamiltonian formalisms Autonomous mechanics Symplectic and presymplectic manifolds Lagrange, Funcions de Hamilton, Sistemes de Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry Classificació AMS::55 Algebraic topology::55R Fiber spaces and bundles Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics |
| Sumario: | We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism. |
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