Web of Science: 6 cites, Scopus: 8 cites, Google Scholar: cites
A new approach to the vakonomic mechanics
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
Sadovskaia, Natalia (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II)

Data: 2014
Resum: The aim of this paper is to show that the Lagrange-d'Alembert and its equivalent the Gauss and Appel principle are not the only way to deduce the equations of motion of the nonholonomic systems. Instead of them, here we consider the generalization of the Hamiltonian principle for nonholonomic systems with nonzero transpositional relations. By applying this variational principle which takes into the account transpositional relations different from the classical ones we deduce the equations of motion for the nonholonomic systems with constraints that in general are nonlinear in the velocity. These equations of motion coincide, except perhaps in a zero Lebesgue measure set, with the classical differential equations deduced with d'Alembert-Lagrange principle. We provide a new point of view on the transpositional relations for the constrained mechanical systems: the virtual variations can produce zero or non-zero transpositional relations. In particular the independent virtual variations can produce non-zero transpositional relations. For the unconstrained mechanical systems the virtual variations always produce zero transpositional relations. We conjecture that the existence of the nonlinear constraints in the velocity must be sought outside of the Newtonian model. All our results are illustrated with precise examples.
Ajuts: Ministerio de Ciencia e Innovación MTM 2008-03437
Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
European Commission 318999
European Commission 316338
Nota: Agraïments: The second author was partly supported by the Spanish Ministry of Education through projects TSI2007-65406-C03-01 "E-AEGIS" and Consolider CSD2007-00004 "ARES"
Drets: Tots els drets reservats.
Llengua: Anglès
Document: Article ; recerca ; Versió acceptada per publicar
Matèria: Chapligyn system ; Constrained Lagrangian system ; D' Alembert-Lagrange principle ; Equation of motion ; Generalized Hamiltonian principle ; Newtonian model ; Transpositional relations ; Vakonomic mechanic ; Variational principle ; Vorones system
Publicat a: Nonlinear Dynamics, Vol. 78 (2014) , p. 2219-2247, ISSN 1573-269X

DOI: 10.1007/s11071-014-1554-3

39 p, 790.9 KB

El registre apareix a les col·leccions:
Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
Articles > Articles de recerca
Articles > Articles publicats

 Registre creat el 2016-05-06, darrera modificació el 2022-02-13

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