A new perspective on nonholonomic brackets and Hamilton–Jacobi theory
The nonholonomic dynamics can be described by the so-called nonholonomic bracket on the constrained submanifold, which is a non-integrable modification of the Poisson bracket of the ambient space, in this case, of the canonical bracket on the cotangent bundle of the configuration manifold. This brac...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/380818 |
| Acceso en línea: | http://hdl.handle.net/10261/380818 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85184506305&doi=10.1016%2fj.geomphys.2024.105116&partnerID=40&md5=dc8d9007f4b37b7be3a65fa0402ed31b |
| Access Level: | acceso abierto |
| Palabra clave: | Almost Poisson brackets Hamilton–Jacobi equation Nonholonomic mechanics Skew-symmetric algebroids |
| Sumario: | The nonholonomic dynamics can be described by the so-called nonholonomic bracket on the constrained submanifold, which is a non-integrable modification of the Poisson bracket of the ambient space, in this case, of the canonical bracket on the cotangent bundle of the configuration manifold. This bracket was defined in [6,21] although there was already some particular and less direct definition. On the other hand, another bracket, also called nonholonomic bracket, was defined using the description of the problem in terms of skew-symmetric algebroids [13,20]. Recently, reviewing two older papers by R. J. Eden [17,18], we have defined a new bracket which we call Eden bracket. In the present paper, we prove that these three brackets coincide. Moreover, the description of the nonholonomic bracket à la Eden has allowed us to make important advances in the study of Hamilton–Jacobi theory and the quantization of nonholonomic systems. © 2024 The Authors |
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