Integrable geodesic flows on the sphere, generated by Goryachev-Chaplygin and Kowalewski systems in the dynamics of a rigid body (Q1905271)
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scientific article; zbMATH DE number 830715
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Integrable geodesic flows on the sphere, generated by Goryachev-Chaplygin and Kowalewski systems in the dynamics of a rigid body |
scientific article; zbMATH DE number 830715 |
Statements
Integrable geodesic flows on the sphere, generated by Goryachev-Chaplygin and Kowalewski systems in the dynamics of a rigid body (English)
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8 January 1996
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We explicitly construct Riemannian metrics on \(S^2\) corresponding to the two classical Kowalewski and Goryachev-Chaplygin integrable cases, and we show that the first integrals of the corresponding geodesic flows (whose orders are 4 and 3 respectively) do not reduce to linear and quadratic ones.
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Euler-Poisson equations
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Maupertuis' principle
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Riemannian metrics
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first integrals
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