Estudo sobre a teoria de vínculos de Hamilton-Jacobi
The Hamilton-Jacobi theory is usually presented as an extension of the Hamilton's theory through the canonical transformations. However, the mathematician Constantin Carathéodory showed this theory, its existence and validity, is independent of the Hamiltonian formalism. In this work, we presen...
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| Formato: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2013 |
| País: | Brasil |
| Recursos: | Universidade Estadual Paulista (UNESP) |
| Repositorio: | Repositório Institucional da UNESP |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.unesp.br:11449/132007 |
| Acesso em linha: | http://hdl.handle.net/11449/132007 http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/28-10-2015/000852795.pdf |
| Access Level: | acceso abierto |
| Palavra-chave: | Princípios variacionais Hamilton-Jacobi, Equações Termodinamica Variational principles |
| Resumo: | The Hamilton-Jacobi theory is usually presented as an extension of the Hamilton's theory through the canonical transformations. However, the mathematician Constantin Carathéodory showed this theory, its existence and validity, is independent of the Hamiltonian formalism. In this work, we present the Caratheodory's approach to the Hamilton-Jacobi theory. From this procedure, we build a theory of constraints which can solve problems with involutive and non-involutive constraints. For this, we analyze the integrability of the equations and introduce the operation of the generalized brackets that, instead of Poisson brackets, will describe the dynamics of constrained systems. We show an application of this theory in BF model of the field theory. Finally, we will discuss the Carathéodory's Axiomatic Thermodynamics and also show the Hamilton-Jacobi theory in Thermodynamics, which is valid to illustrate the wide coverage of this formalism |
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