Geodesic
Invariants of systems having a small number of degrees of freedom with dissipation
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2024), pp. 3-15

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Tensor invariants (differential forms) for homogeneous dynamical systems on tangent bundles to smooth two-dimensional manifolds are presented in the paper. The connection between the presence of these invariants and the full set of first integrals necessary for integration of geodesic, potential, and dissipative systems is shown. At the same time, the introduced force fields make the considered systems dissipative with dissipation of different signs and generalize the previously considered ones. We represent the typical examples from rigid body dynamics. 
@article{VMUMM_2024_2_a0,
     author = {M. V. Shamolin},
     title = {Invariants of systems having a small number of degrees of freedom with dissipation},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {3--15},
     publisher = {mathdoc},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2024_2_a0/}
}
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M. V. Shamolin. Invariants of systems having a small number of degrees of freedom with dissipation. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2024), pp. 3-15. http://geodesic.mathdoc.fr/item/VMUMM_2024_2_a0/