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

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  • H. M. Yehia
  • A. A. Elmandouh

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.

Suggested Citation

  • H. M. Yehia & A. A. Elmandouh, 2016. "Integrable 2D Time-Irreversible Systems with a Cubic Second Integral," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-10, May.
    • Handle: RePEc:hin:jnlamp:8958747
    DOI: 10.1155/2016/8958747
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