Note on integrability of certain homogeneous Hamiltonian systems
  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. 
Wojciech Szumi\'nski, A. J. Maciejewski and Maria Przybylska
nlin.SI math-ph math.MP