Abstract
In this paper, we prove the integrability of certain classes of dynamical systems on the tangent bundles of four-dimensional manifolds (systems with four degrees of freedom). The force field considered possessed so-called variable dissipation; they are generalizations of fields studied earlier. This paper continues earlier works of the author devoted to systems on the tangent bundles of two- and three-dimensional manifolds.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 150, Geometry and Mechanics, 2018.
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Shamolin, M.V. Examples of Integrable Systems with Dissipation on the Tangent Bundles of Four-Dimensional Manifolds. J Math Sci 250, 973–983 (2020). https://doi.org/10.1007/s10958-020-05057-9
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DOI: https://doi.org/10.1007/s10958-020-05057-9
Keywords and phrases
- multidimensional dynamical system
- nonconservative force field
- integrability
- transcendental first integral