Integrable 2D Time-Irreversible Systems with a Cubic Second Integral

H. M. Yehia and A. A. Elmandouh

Advances in Mathematical Physics, 2016, vol. 2016, 1-10

Abstract:

We construct a very rare integrable 2D mechanical system which admits a complementary integral of motion cubic in the velocities in the presence of conservative potential and velocity-dependent (gyroscopic) forces. Special cases are given interpretation as a motion of a particle on a sphere endowed with a Riemannian metric, a particle in the Euclidean plane, and new generalizations of two cases of motion of a rigid body with a cubic integral, known by names of Goriachev-Chaplygin and Goriachev.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:8958747

DOI: 10.1155/2016/8958747

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