Note on integrability of certain homogeneous Hamiltonian systems (1606.03023v1)

Published 9 Jun 2016 in nlin.SI, math-ph, and math.MP

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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