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On Killing tensors in three-dimensional Euclidean space

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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.

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Notes

  1. Position-dependent mass systems.

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Funding

The study was supported by the Russian Science Foundation (grant No. 21-11-00141).

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Correspondence to A. V. Tsiganov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2022, Vol. 212, pp. 149–164 https://doi.org/10.4213/tmf10248.

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Tsiganov, A.V. On Killing tensors in three-dimensional Euclidean space. Theor Math Phys 212, 1019–1032 (2022). https://doi.org/10.1134/S0040577922070108

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  • DOI: https://doi.org/10.1134/S0040577922070108

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