dorsal/arxiv
View SchemaConstrained Systems and Analytical Mechanics in Spases with Torsion
| Authors | Sergei V. Shabanov |
|---|---|
| Categories | |
| ArXiv ID | physics/9801023 |
| URL | https://arxiv.org/abs/physics/9801023 |
| DOI | 10.1088/0305-4470/31/22/016 |
| Journal | J.Phys.A31:5177-5190,1998 |
Abstract
A system with anholonomic constraints where the trajectories of physical degrees of freedom are autoparallels on a manifold equipped with a general Cartan connection is discussed. A variational principle for the autoparallel trajectories is derived from the d'Alambert-Lagrange principle for anholonomic constrained systems. A geometrical (coordinate-independent) formulation of the variational principle is given. Its relation to Sedov's anholonomic variational principle for dissipative systems and to Poincar\'e's variational principle in anholonomic reference frames is established. A modification of Noether's theorem due to the torsion force is studied. A non-local action whose extrema contain the autoparallels is proposed. The action can be made local by adding auxiliary degrees of freedom coupled to the original variables in a special way.
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"abstract": "A system with anholonomic constraints where the trajectories of physical\ndegrees of freedom are autoparallels on a manifold equipped with a general\nCartan connection is discussed. A variational principle for the autoparallel\ntrajectories is derived from the d\u0027Alambert-Lagrange principle for anholonomic\nconstrained systems. A geometrical (coordinate-independent) formulation of the\nvariational principle is given. Its relation to Sedov\u0027s anholonomic variational\nprinciple for dissipative systems and to Poincar\\\u0027e\u0027s variational principle in\nanholonomic reference frames is established. A modification of Noether\u0027s\ntheorem due to the torsion force is studied. A non-local action whose extrema\ncontain the autoparallels is proposed. The action can be made local by adding\nauxiliary degrees of freedom coupled to the original variables in a special\nway.",
"arxiv_id": "physics/9801023",
"authors": [
"Sergei V. Shabanov"
],
"categories": [
"math-ph",
"gr-qc",
"math.MP",
"quant-ph"
],
"doi": "10.1088/0305-4470/31/22/016",
"journal_ref": "J.Phys.A31:5177-5190,1998",
"title": "Constrained Systems and Analytical Mechanics in Spases with Torsion",
"url": "https://arxiv.org/abs/physics/9801023"
},
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