Title:
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On the dinamics of nonholonomic systems
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Author:
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Ramírez Inostroza, Rafael Orlando; Sadovskaia Nurimanova, Natalia Guennadievna
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. MMAC - Models Matemàtics aplicats a les ciencies humanes i de la natura |
Abstract:
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In the development of nonholonomic mechanics one can observe recurring confusion over
the very equations of motion as well as the deeper questions associated with the geometry
and analysis of these equations. First of all, as far as the equations of motion themselves are concerned, the confusion mainly centered on whether or not the equations could be derived from a variational principle in the usual sense.
Attempting to dissipate this confusion, in the present paper we deduce a new form of
equations of motion which are suitable for both nonholonomic systems with either linear or nonlinear constraints and holonomic systems (A-model). These equations are deduced from the principle of stationary action (or Hamiltonian principle) with nonzero transpositional relations.
We show that the well-known equations of motion for nonholonomic and holonomic systems
can be deduced from the A-model. For the systems which we call the generalized Vorones-Chaplygin systems we deduce the
equations of motion which coincide with the Vorones and Chaplygin equations for the case in which the constraints are linear with respect to the velocity.
An additional result is that the transpositional relations are different from zero only for those generalized coordinates whose variations (in accordance with the equations of nonholonomic constraints) are dependent. For the remaining coordinates, the transpositional relations may be zero. |
Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències -Nonholonomic dynamical systems -Equations of motion -Constraints (Physics) -Hamiltonian systems -Mechanics -Dinàmica -Hamilton, Sistemes de -Mecànica -Moviment |
Rights:
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Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
Document type:
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Article - Published version Article |
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