Geodesic
Complete list of first integrals for dynamic equations of motion of a solid body in a resisting medium with consideration of linear damping
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2012), pp. 44-47

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A new case of integrability in the spatial problem of rigid body motion with consideration of the nonconservative moment of forces is discussed. A nonconservative force field of action of the medium on the body is constructed. Contrary to some previous author's works, a linear dependence of this field on the angular velocity is taken into account, although the introducing of this dependence into the components of such a field is not obvious. 
@article{VMUMM_2012_4_a7,
     author = {M. V. Shamolin},
     title = {Complete list of first integrals for dynamic equations of motion of a solid body in a resisting medium with consideration of linear damping},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {44--47},
     publisher = {mathdoc},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_4_a7/}
}
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M. V. Shamolin. Complete list of first integrals for dynamic equations of motion of a solid body in a resisting medium with consideration of linear damping. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2012), pp. 44-47. http://geodesic.mathdoc.fr/item/VMUMM_2012_4_a7/