Inverse Approach in Ordinary Differential Equations: Applications to Lagrangian and Hamiltonian Mechanics

Jaume Llibre, Rafael Ramírez, Natalia Sadovskaia

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7 Citations (Scopus)

Abstract

© 2014, Springer Science+Business Media New York. This paper is on the so called inverse problem of ordinary differential equations, i.e. the problem of determining the differential system satisfying a set of given properties. More precisely we characterize under very general assumptions the ordinary differential equations in (Formula Presented.) which have a given set of either (Formula Presented.) partial integrals, or (Formula Presented.) first integral, or (Formula Presented.) partial and first integrals. Moreover, for such systems we determine the necessary and sufficient conditions for the existence of (Formula Presented.) independent first integrals. We give two relevant applications of the solutions of these inverse problem to constrained Lagrangian and Hamiltonian systems respectively. Additionally we provide the general solution of the inverse problem in dynamics.
Original languageEnglish
Pages (from-to)529-581
JournalJournal of Dynamics and Differential Equations
Volume26
Issue number3
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • 16th Hilbert’s problem
  • Algebraic limit circles
  • Darboux integrability
  • Invariant algebraic circles
  • Invariant circles
  • Polynomial planar differential system
  • Polynomial vector fields

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