Geodesic
Systems with~dissipation with~five degrees of freedom: Analysis and integrability. II. Dynamical systems on tangent bundles
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 2, Tome 209 (2022), pp. 88-107

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The work contains the second and third parts of the survey on the integrability of systems with five degrees of freedom (the first part: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 208, (2022), pp. 91–121). In the first part, the primordial problem from the dynamics of a multidimensional rigid body placed in a nonconservative force field was described in detail. In the second and third parts, we consider more general dynamical systems on tangent bundles to the five-dimensional sphere and other 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 five degrees of freedom, integrability, transcendental first integral. 
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     author = {M. V. Shamolin},
     title = {Systems with~dissipation with~five degrees of freedom: {Analysis} and integrability. {II.} {Dynamical} systems on tangent bundles},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {88--107},
     publisher = {mathdoc},
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M. V. Shamolin. Systems with~dissipation with~five degrees of freedom: Analysis and integrability. II. Dynamical systems on tangent bundles. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 2, Tome 209 (2022), pp. 88-107. http://geodesic.mathdoc.fr/item/INTO_2022_209_a7/