Geodesic
Examples of Integrable Systems with Dissipation on the Tangent Bundles of Multidimensional Spheres
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 150 (2018), pp. 78-87

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In this paper, we prove the integrability of certain classes of dynamical systems that appear in the dynamics of multidimensional rigid bodies and the dynamics of a particle moving on a multidimensional sphere. Force field considered have the so-called variable dissipation with zero mean; they are generalizations of fields studied earlier. We present examples of the application of the method for integrating dissipative systems on the tangent bundles of two-dimensional surfaces of revolution.
Keywords: dynamical system, nonconservative force field, integrability, transcendental first integral. 
@article{INTO_2018_150_a3,
     author = {M. V. Shamolin},
     title = {Examples of {Integrable} {Systems} with {Dissipation} on the {Tangent} {Bundles} of {Multidimensional} {Spheres}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {78--87},
     publisher = {mathdoc},
     volume = {150},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_150_a3/}
}
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M. V. Shamolin. Examples of Integrable Systems with Dissipation on the Tangent Bundles of Multidimensional Spheres. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 150 (2018), pp. 78-87. http://geodesic.mathdoc.fr/item/INTO_2018_150_a3/