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On the inverse problem in the Hamiltonian formalism for a system of second-order ODEs
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  • Ahmad Al-Dweik,
  • Marwan Aloqeili,
  • Ivar Ekeland,
  • Gerard Thompson,
  • Fazal Mahomed
Ahmad Al-Dweik
Birzeit University
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Marwan Aloqeili
Birzeit University
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Ivar Ekeland
Universite Paris Dauphine
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Gerard Thompson
The University of Toledo
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Fazal Mahomed
University of the Witwatersrand Johannesburg

Corresponding Author:fazal.mahomed@wits.ac.za

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Abstract

Two procedures for finding a Hamiltonian for a system of n second-order ODEs, without determining any of its first integrals, are provided. The first procedure is based on the existence of a regular Lagrangian, while the second is based on the existence of a closed invariant two-form of maximal rank. Examples are given to illustrate these procedures.