On Killing tensors in three-dimensional Euclidean space View Full Text


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Article Info

DATE

2022-07-26

AUTHORS

A. V. Tsiganov

ABSTRACT

We discuss the properties of second-order Killing tensors in three-dimensional Euclidean space that guarantee the existence of a third integral of motion ensuring the Liouville integrability of the corresponding equations of motion. We prove that in addition to the linear Noether and quadratic Stäckel integrals of motion, there are integrable systems with two quadratic integrals of motion and one fourth-order integral of motion in momenta. A generalization to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}-dimensional case and to deformations of the standard flat metric is proposed. More... »

PAGES

1019-1032

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/s0040577922070108

DOI

http://dx.doi.org/10.1134/s0040577922070108

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1149789422


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