Geodesic
New cases of integrability of systems of geodesics and potential and dissipative systems on tangent bundles of finite-dimensional manifolds
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 78-86

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The integrability of certain classes of homogeneous geodesic, potential, and dissipative dynamical systems on the tangent bundles of finite-dimensional manifolds is shown. In this case, the force fields lead to variable-sign dissipation and generalize previously considered fields.
Keywords: dynamical system, geodesics, potential, integrability, dissipation, transcendental first integral. 
@article{DANMA_2021_500_a14,
     author = {M. V. Shamolin},
     title = {New cases of integrability of systems of geodesics and potential and dissipative systems on tangent bundles of finite-dimensional manifolds},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {78--86},
     publisher = {mathdoc},
     volume = {500},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_500_a14/}
}
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M. V. Shamolin. New cases of integrability of systems of geodesics and potential and dissipative systems on tangent bundles of finite-dimensional manifolds. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 78-86. http://geodesic.mathdoc.fr/item/DANMA_2021_500_a14/