Note on integrability of certain homogeneous Hamiltonian systems

2016/06/09 by Wojciech Szumiński, A. J. Maciejewski, Maria Przybylska · 1 citation
Physics and Astronomy · Mathematics · #nlin.SI #math-ph #math.MP

paper · pdf · doi:10.1016/j.physleta.2015.08.032

published as Phys. Lett. A, vol. 379 no 45-46, 2970-2976, 2015

arxiv created 2016/06/09 · arxiv updated 2016/06/10

Abstract

In this paper we investigate a class of natural Hamiltonian systems with two degrees of freedom. The kinetic energy depends on coordinates but the system is homogeneous. Thanks to this property it admits, in a general case, a particular solution. Using this solution we derive necessary conditions for the integrability of such systems investigating differential Galois group of variational equations.

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