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)

Date:	2014
Abstract:	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).
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	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".
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Hamiltonian Mechanics ; Inverse problems ; Lagrangian Mechanics
Published in:	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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