Integrable 2D Time-Irreversible Systems with a Cubic Second Integral
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...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/8958747 |
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| author | H. M. Yehia A. A. Elmandouh |
| author_facet | H. M. Yehia A. A. Elmandouh |
| author_sort | H. M. Yehia |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-fcc87f321a6f457b82619832ce785306 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-fcc87f321a6f457b82619832ce7853062025-02-03T01:31:18ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/89587478958747Integrable 2D Time-Irreversible Systems with a Cubic Second IntegralH. M. Yehia0A. A. Elmandouh1Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptWe 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.http://dx.doi.org/10.1155/2016/8958747 |
| spellingShingle | H. M. Yehia A. A. Elmandouh Integrable 2D Time-Irreversible Systems with a Cubic Second Integral Advances in Mathematical Physics |
| title | Integrable 2D Time-Irreversible Systems with a Cubic Second Integral |
| title_full | Integrable 2D Time-Irreversible Systems with a Cubic Second Integral |
| title_fullStr | Integrable 2D Time-Irreversible Systems with a Cubic Second Integral |
| title_full_unstemmed | Integrable 2D Time-Irreversible Systems with a Cubic Second Integral |
| title_short | Integrable 2D Time-Irreversible Systems with a Cubic Second Integral |
| title_sort | integrable 2d time irreversible systems with a cubic second integral |
| url | http://dx.doi.org/10.1155/2016/8958747 |
| work_keys_str_mv | AT hmyehia integrable2dtimeirreversiblesystemswithacubicsecondintegral AT aaelmandouh integrable2dtimeirreversiblesystemswithacubicsecondintegral |