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arXiv · 1606.03023

Note on integrability of certain homogeneous Hamiltonian systems

Wojciech Szumiński·A. J. Maciejewski·Maria Przybylska
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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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Wojciech Szumiński, A. J. Maciejewski, Maria Przybylska. 2016-06-09. Note on integrability of certain homogeneous Hamiltonian systems. https://doi.org/10.1016/j.physleta.2015.08.032

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