Second order Killing tensors related to symmetric spaces
Exactly Solvable and Integrable Systems
2023-07-19 v4 Mathematical Physics
Dynamical Systems
math.MP
Abstract
We discuss the pairs of quadratic integrals of motion belonging to the -dimensional space of independent integrals of motion in involution, that provide integrability of the corresponding Hamiltonian equations of motion by quadratures. In contrast to the Eisenhart theory, additional integrals of motion are polynomials of the fourth, sixth and other orders in momenta. The main focus is on the second-order Killing tensors corresponding to quadratic integrals of motion and relating to the special combinations of rotations and translations in Euclidean space.
Keywords
Cite
@article{arxiv.2301.02774,
title = {Second order Killing tensors related to symmetric spaces},
author = {E. O. Porubov and A. V. Tsiganov},
journal= {arXiv preprint arXiv:2301.02774},
year = {2023}
}
Comments
27 pages, LaTeX with amsfonts