Integrable geodesic flows on the sphere, generated by Goryachev-Chaplygin and Kowalewski systems in the dynamics of a rigid body
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.
scientific article; zbMATH DE number 830715