Geodesic
Odd-order integrable dynamical systems with dissipation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 174 (2020), pp. 52-69

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In this paper, we prove the integrability of some classes of odd-order dynamical systems (namely, systems of order 3, 5, and 7), which are homogeneous in some variables and contain a system on the tangent bundle of a smooth manifolds. In this case, we separate force fields into internal (conservative) and external, which has sign-alternating dissipation. External fields are introduced by using some unimodular transformations and generalize fields considered earlier.
Keywords: dynamical system, nonconservative force field, integrability, transcendental first integral. 
@article{INTO_2020_174_a5,
     author = {M. V. Shamolin},
     title = {Odd-order integrable dynamical systems with dissipation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {52--69},
     publisher = {mathdoc},
     volume = {174},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_174_a5/}
}
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M. V. Shamolin. Odd-order integrable dynamical systems with dissipation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 174 (2020), pp. 52-69. http://geodesic.mathdoc.fr/item/INTO_2020_174_a5/