Geodesic
Systems with~dissipation with~a finite number of degrees of freedom: analysis and ~integrability. II. General class of dynamical systems on the tangent bundle of a multidimensional sphere
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 212 (2022), pp. 139-148

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This paper is the second part of a survey on the integrability of systems with a large number $n$ of degrees of freedom (the first part: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 211 (2022), pp. 41–74). The review consists of three parts. In the first part, the primordial problem from the dynamics of a multidimensional rigid body placed in a nonconservative force field is described in detail. In this second part, we consider more general dynamical systems on the tangent bundles to the $n$-dimensional sphere. In the third part, which will be published in the next issue, we will consider dynamical systems on the tangent bundles to smooth manifolds of a sufficiently wide class. Theorems on sufficient conditions for the integrability of the considered dynamical systems in the class of transcendental functions are proved.
Keywords: dynamical system with a large number of degrees of freedom, integrability, transcendental first integral. 
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     author = {M. V. Shamolin},
     title = {Systems with~dissipation with~a finite number of degrees of freedom: analysis and ~integrability.  {II.} {General} class of dynamical systems on the tangent bundle of a multidimensional sphere},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {139--148},
     publisher = {mathdoc},
     volume = {212},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_212_a13/}
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M. V. Shamolin. Systems with~dissipation with~a finite number of degrees of freedom: analysis and ~integrability.  II. General class of dynamical systems on the tangent bundle of a multidimensional sphere. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 212 (2022), pp. 139-148. http://geodesic.mathdoc.fr/item/INTO_2022_212_a13/