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This article is cited in 4 scientific papers (total in 4 papers)
On Killing tensors in three-dimensional Euclidean space
A. V. Tsiganov Saint-Petersburg State University, Saint-Petersburg,
Russia
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 $n$-dimensional case and to deformations of the standard flat metric is proposed.
Keywords:
Hamilton–Jacobi equations, separation of variables, Killing tensors.
Received: 14.01.2022 Revised: 14.01.2022
Citation:
A. V. Tsiganov, “On Killing tensors in three-dimensional Euclidean space”, TMF, 212:1 (2022), 149–164; Theoret. and Math. Phys., 212:1 (2022), 1019–1032
Linking options:
https://www.mathnet.ru/eng/tmf10248https://doi.org/10.4213/tmf10248 https://www.mathnet.ru/eng/tmf/v212/i1/p149
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