Note on integrability of certain homogeneous Hamiltonian systems
Exactly Solvable and Integrable Systems
2016-06-10 v1 Mathematical Physics
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.
Cite
@article{arxiv.1606.03023,
title = {Note on integrability of certain homogeneous Hamiltonian systems},
author = {Wojciech Szumiński and A. J. Maciejewski and Maria Przybylska},
journal= {arXiv preprint arXiv:1606.03023},
year = {2016}
}