Geodesic
About destabilization of equilibrium point is caused by linear and quadratic forces of viscous friction
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 3, pp. 49-60

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Holonomic systems with two degrees of freedom are considered. It is supposed that potential forces, non-conservative positional forces, linear and quadratic dissipative forces act in these systems. The normal form of equations of motion is obtained and averaged in non-resonance case. In particular case when quadratic friction forces act independently along main coordinate axes, averaged system is completely investigated. Unique stationary mode of averaged system is obtained and stability of that mode is investigated. Conditions for the existence of an invariant torus and weak instability of equilibrium position are obtained.
Keywords: Zigler’s effect, non-conservative positional force, linear dissipative force, quadratic dissipative force, Raileigh’s function, normalization method of Hori-Kamel
Mots-clés : invariant torus. 
@article{SVMO_2016_18_3_a4,
     author = {A. Yu. Mayorov},
     title = {About destabilization of equilibrium point is caused by linear and quadratic forces of viscous friction},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {49--60},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2016_18_3_a4/}
}
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A. Yu. Mayorov. About destabilization of equilibrium point is caused by linear and quadratic forces of viscous friction. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 3, pp. 49-60. http://geodesic.mathdoc.fr/item/SVMO_2016_18_3_a4/