Almost-Poisson Brackets for Nonholonomic Systems with Gyroscopic Terms and Hamiltonisation
We extend known constructions of almost-Poisson brackets and their gauge transformations to nonholonomic systems whose Lagrangian is not mechanical but possesses a gyroscopic term linear in the velocities. The new feature introduced by such a term is that the Legendre transformation is an affine, in...
| 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:10261/380817 |
| Acceso en línea: | http://hdl.handle.net/10261/380817 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85205733153&doi=10.1007%2fs00332-024-10084-w&partnerID=40&md5=57fa1c40b0a92d05670461598329fdc5 |
| Access Level: | acceso abierto |
| Palabra clave: | 37J60 53Z05 70E55 70G45 Almost-Poisson brackets Suslov problem Chaplygin sphere Nonholonomic systems Gauge transformations Gyroscopic Lagrangian Hamiltonisation |
| Sumario: | We extend known constructions of almost-Poisson brackets and their gauge transformations to nonholonomic systems whose Lagrangian is not mechanical but possesses a gyroscopic term linear in the velocities. The new feature introduced by such a term is that the Legendre transformation is an affine, instead of linear, bundle isomorphism between the tangent and cotangent bundles of the configuration space and some care is needed in the development of the geometric formalism. At the end of the day, the affine nature of the Legendre transform is reflected in the affine dependence of the brackets that we construct on the momentum variables. Our study is motivated by a wide class of nonholonomic systems involving rigid bodies with internal rotors which are of interest in control. Our construction provides a natural geometric framework for the (known) Hamiltonisations of the gyrostatic generalisations of the Suslov and Chaplygin sphere problems. © The Author(s) 2024. |
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