Geodesic
Auto-oscillations under the braking of a~rigid body in a~resisting medium
Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 4, pp. 90-102

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We carry out a qualitative analysis of the rectilinear and spatial problems of the motion of rigid bodies in a resisting media. We construct a nonlinear model of the impact of the medium on the rigid body taking into account the dependence of the arm of force on the reduced angular velocity of the body. In this case, the moment of the force is also a function of the angle of the attack. As was shown by processing the experimental data on the motion of homogeneous circular cylinders in water, these circumstances should be taken into account in the simulation. The analysis of the plane and space models of the interaction of a rigid body with a medium reveal sufficient conditions for the stability of the key motion regime, i.e., of the translational rectilinear braking. We show that, under certain conditions, the presence of a stable or unstable auto-oscillating regime in the system is possible.
Keywords: rigid body, resisting medium, translational rectilinear braking
Mots-clés : auto-oscillations. 
@article{SJIM_2017_20_4_a10,
     author = {M. V. Shamolin},
     title = {Auto-oscillations under the braking of a~rigid body in a~resisting medium},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {90--102},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2017_20_4_a10/}
}
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M. V. Shamolin. Auto-oscillations under the braking of a~rigid body in a~resisting medium. Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 4, pp. 90-102. http://geodesic.mathdoc.fr/item/SJIM_2017_20_4_a10/