Integrable 2D Time-Irreversible Systems with a Cubic Second Integral-Reference-Cited by-同舟云学术

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

Published:2016 Issue: Volume:2016 Page:1-10
ISSN:1687-9120
Container-title:Advances in Mathematical Physics
language:en
Short-container-title:Advances in Mathematical Physics

Author:

Yehia H. M.¹,Elmandouh A. A.¹²

Affiliation:

1. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

2. Faculty of Science, Mathematics Department, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia

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.

Publisher

Hindawi Limited

Subject

Applied Mathematics,General Physics and Astronomy

Link

http://downloads.hindawi.com/journals/amp/2016/8958747.pdf

Reference35 articles.

1. Compatibility conditions for a non-quadratic integral of motion

2. Integrability of Hamiltonians with third‐ and fourth‐degree polynomial potentials

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