Geodesic
New cases of integrable systems with dissipation on tangent bundles of multidimensional spheres
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 137 (2017), pp. 104-117 Cet article a éte moissonné depuis la source Math-Net.Ru

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In many problems of multidimensional dynamics, systems appear whose state spaces are spheres of finite dimension. Clearly, phase spaces of such systems are tangent bundles of these spheres. In this paper, we examine nonconservative force field in the dynamics of a multidimensional rigid body in which the system possesses a complete set of first integrals that can be expressed as finite combinations of elementary transcendental functions. We consider the case where the moment of nonconservative forces depends on the tensor of angular velocity.
Keywords: dynamical system, dissipation, transcendental first integral, integrability. 
@article{INTO_2017_137_a6,
     author = {M. V. Shamolin},
     title = {New cases of integrable systems with dissipation on 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 = {104--117},
     year = {2017},
     volume = {137},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_137_a6/}
}
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M. V. Shamolin. New cases of integrable systems with dissipation on tangent bundles of multidimensional spheres. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 137 (2017), pp. 104-117. http://geodesic.mathdoc.fr/item/INTO_2017_137_a6/