Geodesic
On the stability of solutions of dynamical systems with dissipation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 202 (2021), pp. 114-125

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Many authors analyzed plane-parallel and spatial motions of realistic rigid bodies in various media. Numerous nonlinear models of the interaction of media and rigid bodies were constructed. For plane-parallel and spatial models, sufficient conditions for the stability of the rectilinear translational motion were found. We prove that under some conditions, such systems may also possess self-oscillating regimes, both stable or unstable. We discuss a natural generalization of force fields in various dissipative dynamical systems with one and two degrees of freedom.
Keywords: dynamic system, dissipation, stability in the Lyapunov sense. 
@article{INTO_2021_202_a5,
     author = {M. V. Shamolin},
     title = {On the stability of solutions of 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 = {114--125},
     publisher = {mathdoc},
     volume = {202},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_202_a5/}
}
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M. V. Shamolin. On the stability of solutions of dynamical systems with dissipation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 202 (2021), pp. 114-125. http://geodesic.mathdoc.fr/item/INTO_2021_202_a5/