Geodesic
Integrable homogeneous dynamical systems with dissipation on the tangent bundles of smooth finite-dimensional manifolds. II. Equations of motion on the tangent bundle of an $n$-dimensional manifold in a potential force field
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 215 (2022), pp. 81-94

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This paper is the second part of the work on the integrability of general classes of homogeneous dynamical systems with variable dissipation on the tangent bundles of $n$-dimensional manifolds. The first part of the paper is: Integrable homogeneous dynamical systems with dissipation on the tangent bundles of smooth finite-dimensional manifolds. I. Equations of geodesics on the tangent bundle of a smooth $n$-dimensional manifold// Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 214 (2022), pp. 82–106.
Keywords: dynamical system, nonconservative field, integrability, transcendental first integral. 
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     author = {M. V. Shamolin},
     title = {Integrable homogeneous dynamical systems with dissipation on the tangent bundles of smooth finite-dimensional manifolds. {II.} {Equations} of motion on the tangent bundle of an $n$-dimensional manifold in a potential force field},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     volume = {215},
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M. V. Shamolin. Integrable homogeneous dynamical systems with dissipation on the tangent bundles of smooth finite-dimensional manifolds. II. Equations of motion on the tangent bundle of an $n$-dimensional manifold in a potential force field. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 215 (2022), pp. 81-94. http://geodesic.mathdoc.fr/item/INTO_2022_215_a8/