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http://dspace.mediu.edu.my:8181/xmlui/handle/10261/2281| Title: | A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids |
| Keywords: | Lie algebroids Lie affgebroids Lagrangian Mechanics Hamiltonian Mechanics Nonholonomic Mechanics Lagrange-d’Alembert equations Projectors AV-bundles Aff-Poisson brackets Non-holonomic brackets |
| Publisher: | American Institute of Physics |
| Description: | 50 pages.-- Pre-print archive.-- PACS: 45.05.+x;
02.20.Sv; 02.40.Hw This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity conditions that guarantee that the dynamics of the system can be obtained as a suitable projection of the unconstrained dynamics. It is shown that one can define an almost aff-Poisson bracket on the constraint AV-bundle, which plays a prominent role in the description of nonholonomic dynamics. Moreover, these developments give a general description of nonholonomic systems and the unified treatment permits to study nonholonomic systems after or before reduction in the same framework. Also, it is not necessary to distinguish between linear or affine constraints and the methods are valid for explicitly time-dependent systems. This work has been partially supported by MEC (Spain) Grants MTM 2006-03322, MTM 2004-7832, project “Ingenio Mathematica” (i-MATH) No. CSD 2006-00032 (Consolider-Ingenio 2010) and S-0505/ESP/0158 of the CAM. D. Iglesias wants to thank MEC for a Research Contract “Juan de la Cierva”. Peer reviewed |
| URI: | http://dspace.mediu.edu.my:8181/xmlui/handle/10261/2281 |
| Other Identifiers: | arXiv:0705.0278v1 Journal of Mathematical Physics 48(8): 083513 (2007) 0022-2488 http://hdl.handle.net/10261/2281 10.1063/1.2776845 |
| Appears in Collections: | Digital Csic |
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