Higher order first integrals of autonomous dynamical systems
Abstract
A theorem is derived which determines higher order first integrals of autonomous holonomic dynamical systems in a general space, provided the collineations and the Killing tensors up to the order of the first integral of the kinetic metric, defined by the kinetic energy of the system, can be computed. The theorem is applied in the case of Newtonian autonomous conservative dynamical systems of two degrees of freedom, where known and new integrable and superintegrable potentials that admit cubic first integrals are determined.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 December 2021
 DOI:
 10.1016/j.geomphys.2021.104383
 arXiv:
 arXiv:2110.02326
 Bibcode:
 2021JGP...17004383M
 Keywords:

 Liouville integrable system;
 Superintegrable system;
 Higher order first integral;
 Kinetic metric;
 Killing tensor;
 Cubic first integral;
 Mathematical Physics
 EPrint:
 Journal of Geometry and Physics 170, 104383 (2021)