Geodesic
Integrable systems on the tangent bundle of a multi-dimensional sphere
Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 31 (2016) no. 31, pp. 257-323

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This paper contains a systematic exposition of some results on the equations of motion of a dynamically symmetric $n$-dimensional rigid body in a nonconservative field of forces. Similar bodies are considered in the dynamics of actual rigid bodies interacting with a resisting medium under the conditions of jet flow past the body with a nonconservative following force acting on the body in such a way that its characteristic point has a constant velocity, which means that the system has a nonintegrable servo-constraint. 
@article{TSP_2016_31_31_a11,
     author = {M. V. Shamolin},
     title = {Integrable systems on the tangent bundle of a multi-dimensional sphere},
     journal = {Trudy Seminara im. I.G. Petrovskogo},
     pages = {257--323},
     publisher = {mathdoc},
     volume = {31},
     number = {31},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TSP_2016_31_31_a11/}
}
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M. V. Shamolin. Integrable systems on the tangent bundle of a multi-dimensional sphere. Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 31 (2016) no. 31, pp. 257-323. http://geodesic.mathdoc.fr/item/TSP_2016_31_31_a11/