Geodesic
A new case of an integrable system with dissipation on the tangent bundle of a multidimensional sphere
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2018), pp. 34-43

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The equations of motion for a dynamically symmetric $n$-dimensional fixed rigid body-pendulum situated in a nonconservative force field are studied. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of an incident medium. The complete list of (in general) transcendental first integrals expressed in terms of a finite combination of elementary functions is found. 
@article{VMUMM_2018_3_a5,
     author = {M. V. Shamolin},
     title = {A new case of an integrable system with dissipation on the tangent bundle of a multidimensional sphere},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {34--43},
     publisher = {mathdoc},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2018_3_a5/}
}
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M. V. Shamolin. A new case of an integrable system with dissipation on the tangent bundle of a multidimensional sphere. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2018), pp. 34-43. http://geodesic.mathdoc.fr/item/VMUMM_2018_3_a5/