Web of Science: 8 cites, Scopus: 7 cites, Google Scholar: cites
Inverse Approach in Ordinary Differential Equations: Applications to Lagrangian and Hamiltonian 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: This paper is on the so called inverse problem of ordinary differential systems, i. e. the problem of determining the differential systems satisfying a set of given properties. More precisely, we characterize under very general assumptions the ordinary differential systems in RN which have a given set of either M ≤ N, or M > N partial integrals, or M < N first integrals, or M ≤ N partial and first integrals. Moreover, for such systems we determine the necessary and sufficient conditions for the existence of N − 1 independent first integrals. For the systems with M < N partial integrals we provide sufficient conditions for the existence of a first integral. We give two relevant applications of the solutions of these inverse problems to constrained Lagrangian and constrained Hamiltonian systems. Additionally we provide a particular solution of the inverse problem in dynamics, and give a generalized solution of the problem of integration of the equation of motion in the classical Suslov problem on SO(3).
Ajuts: Ministerio de Economía y Competitividad MTM2008-03437
Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
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: Hamiltonian Mechanics ; Inverse problems ; Lagrangian Mechanics
Publicat a: Journal of dynamics and differential equations, Vol. 26 (2014) , p. 529-581, ISSN 1572-9222

DOI: 10.1007/s10884-014-9390-1


Postprint
52 p, 1.0 MB

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Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
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 Registre creat el 2016-05-06, darrera modificació el 2022-02-13



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