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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - M. V. Shamolin
TI  - Auto-oscillations under the braking of a~rigid body in a~resisting medium
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2017
SP  - 90
EP  - 102
VL  - 20
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2017_20_4_a10/
LA  - ru
ID  - SJIM_2017_20_4_a10
ER  - 
%0 Journal Article
%A M. V. Shamolin
%T Auto-oscillations under the braking of a~rigid body in a~resisting medium
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2017
%P 90-102
%V 20
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2017_20_4_a10/
%G ru
%F SJIM_2017_20_4_a10
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/

[1] Chaplygin S. A., Izbrannye trudy, Nauka, M., 1976 | MR

[2] Shamolin M. V., Metody analiza dinamicheskikh sistem s peremennoi dissipatsiei v dinamike tverdogo tela, Ekzamen, M., 2007

[3] Shamolin M. V., “Dinamicheskie sistemy s peremennoi dissipatsiei: podkhody, metody, prilozheniya”, Fundament. i prikl. matematika, 14:3 (2008), 3–237 | MR | Zbl

[4] Eroshin V. A., Samsonov V. A., Shamolin M. V., “Modelnaya zadacha o tormozhenii tela v soprotivlyayuscheisya srede pri struinom obtekanii”, Izv. RAN. Mekhanika zhidkogo gaza, 1995, no. 3, 23–27

[5] Lamb G., Gidrodinamika, Fizmatgiz, M., 1947

[6] Eroshin V. A., “Eksperimentalnoe issledovanie vkhoda uprugogo tsilindra v vodu s bolshoi skorostyu”, Izv. RAN. Mekhanika zhidkogo gaza, 1992, no. 5, 20–30

[7] Byushgens G. S., Studnev R. V., Dinamika samoleta. Prostranstvennoe dvizhenie, Mashinostroenie, M., 1988

[8] Prandtl L., Betz A., Ergebmisse der Aerodinamischen Versuchsastalt zu Göttingen, Berlin, 1932

[9] Samsonov V. A., Shamolin M. V., Eroshin V. A., Makarshin V. M., Matematicheskoe modelirovanie v zadache o tormozhenii tela v soprotivlyayuscheisya srede pri struinom obtekanii, Nauchnyi otchet In-ta mekhaniki MGU No 4396, In-t mekhaniki MGU, M., 1995

[10] Shamolin M. V., “Semeistvo portretov s predelnymi tsiklami v ploskoi dinamike tverdogo tela, vzaimodeistvuyuschego so sredoi”, Izv. RAN. Mekhanika tverdogo tela, 1998, no. 6, 29–37

[11] Chaplygin S. A., “O dvizhenii tyazhelykh tel v neszhimaemoi zhidkosti”, Poln. sobr. soch., v. 1, Izd-vo AN SSSR, L., 1933, 133–135

[12] Puankare A., O krivykh, opredelyaemykh differentsialnymi uravneniyami, OGIZ, M.–L., 1947

[13] Bautin N. N., Leontovich E. A., Metody i priemy kachestvennogo issledovaniya dinamicheskikh sistem na ploskosti, Nauka, M., 1976 | MR

[14] Shamolin M. V., “Dvizhenie tverdogo tela v soprotivlyayuscheisya srede”, Mat. modelirovanie, 23:12 (2011), 79–104 | MR | Zbl

[15] Shamolin M. V., “Zadacha o dvizhenii tela v soprotivlyayuscheisya srede s uchetom zavisimosti momenta sily soprotivleniya ot uglovoi skorosti”, Mat. modelirovanie, 24:10 (2012), 109–132 | MR