 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| A.A. Burov and E.S. Shalimova, "Bifurcations of Relative Equilibria of a Heavy Bead on a Rotating Parabolic Bowl with Dry Friction," Mech. Solids. 51 (4), 395-405 (2016) |
| Year |
2016 |
Volume |
51 |
Number |
4 |
Pages |
395-405 |
| DOI |
10.3103/S0025654416040038 |
| Title |
Bifurcations of Relative Equilibria of a Heavy Bead on a Rotating Parabolic Bowl with Dry Friction |
| Author(s) |
A.A. Burov (Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia; National Research University "Higher School of Economics," ul. Myasnitskaya 20, Moscow, 101000 Russia, aburov@ccas.ru)
E.S. Shalimova (Lomonosov Moscow State University, Moscow, 119992 Russia, ekateryna-shalimova@yandex.ru) |
| Abstract |
The motion of a heavy bead on the surface of a parabolic bowl rotating at a constant angular velocity about its axis, which coincides with the vertical, is considered. It is assumed that the dry friction force acts between the bead and the bowl. The sets of nonisolated relative equilibria of the bead on the bowl are determined, and their dependence on the problem parameters is studied. The results are illustrated in the form of bifurcation diagrams. |
| Keywords |
systems with friction, relative equilibria, dry friction |
| References |
| 1. | V. V. Krementulo,
"Investigation of the Stability of a Gyroscope Taking into Account
the Dry Friction on the Axis of the Inner Cardan Ring (Gimbal),"
Prikl. Mat. Mekh.
23 (5), 968-970 (1959)
[J. Appl. Math. Mech. (Engl. Transl.)
23 (5), 1382-1386 (1959)]. |
| 2. | V. V. Krementulo,
"Stability of a Gyroscope Having a Vertical Axis of the Outer
Ring with Dry Friction in the Gimbal Axes Taken into Account,"
Prikl. Mat. Mekh.
24 (3), 568-571 (1960)
[J. Appl. Math. Mech. (Engl. Transl.)
24 (3), 843-849 (1960)]. |
| 3. | G. K. Pozharitskii,
"On the Stability of Equilibrium States for Systems with Dry Friction,"
Prikl. Mat. Mekh.
26 (1), 5-14 (1962)
[J. Appl. Math. Mech. (Engl. Transl.)
26 (1), 3-16 (1962)]. |
| 4. | N. Van de Wouw and R. I. Leine,
"Stability of Stationary Sets in Nonlinear Systems with Set-Valued Friction,"
in Proc. 45th IEEE Conf. Decision and Control and European Control Conf. (CDC2006),
San Diego, USA, 2006,
pp. 3765-3770. |
| 5. | R. I. Leine and N. Van de Wouw,
"Stability Properties of Equilibrium Sets of Nonlinear Mechanical Systems
with Dry Friction and Impact,"
Nonlin. Dyn.
51 (4), 551-583 (2008). |
| 6. | R. I. Leine and N. Van de Wouw,
Stability and Convergence of Mechanical Systems with Unilateral Constraints,
in Lect. Notes Appl. Comput. Mech., Vol. 36
(Springer, Berlin, 2008). |
| 7. | R. I. Leine and D. H. Van Compen,
"Bifurcation Phenomena in Non-Smooth Dynamical Systems,"
Eur. J. Chem. A-Solid
25, 595-616 (2006). |
| 8. | R. I. Leine,
"Bifurcations of Equilibria in Non-Smooth Continuous Systems,"
Physica D
223, 121-137 (2006). |
| 9. | A. Teufel, A. Steindl, and H. Troger,
"Classification of Nonsmooth Bifurcations for Oscillator with Friction,"
in Problems of Analytic Mechanics and Stability,
Collection of scientific papers dedicated to the memory of Academician V. V. Rumyantsev
(IPM RAS, Moscow, 2009),
pp. 161-175
[in Russian]. |
| 10. | A. P. Ivanov,
"Bifurcations in Systems with Friction: Basic Methods and Models,"
Nelin. Din.
5 (4), 479-498 (2009). |
| 11. | A. P. Ivanov,
Foundations of Theory of Systems with Friction
(RKhD, Izhevsk, 2011)
[in Russian]. |
| 12. | A. A. Burov,
"On Bifurcations of Relative Equilibria of a Heavy Bead Sliding
with Dry Friction on a Rotating Circle,"
Acta Mech.
212 (3-4), 349-354 (2010). |
| 13. | V. N. Rubanovskii and V. A. Samsonov,
Stability of Steady Motions in Examples and Problems
(Nauka, Moscow, 1988)
[in Russian]. |
| 14. | A. A. Burov and I. A. Yakushev,
"Bifurcations of the Relative Equilibria of a Heavy Bead on a Rotating Hoop with Dry Friction,"
Prikl. Mat. Mekh.
78 (5), 645-655 (2014)
[J. Appl. Math. Mech. (Engl. Transl.)
78 (5), 460-467 (2014)]. |
| 15. | N. Van de Wouw, M. N. van den Heuvel, J. A. van Rooij, and H. Nijmeijer,
"Performance of an Automatic Ball Balancer with dry Friction,"
Int. J. Bifurcat. Chaos
15, 65-82 (2005). |
| 16. | V. V. Kozlov,
"On the Dry-Friction Mechanism,"
Dokl. Ross. Akad. Nauk
437 (6), 766-767 (2011)
[Dokl. Phys. (Engl. Transl.)
56 (4), 256-257 (2011)]. |
| 17. | G. A. Tomlinson,
"A Molecular Theory of Friction,"
Lond. Edinb. Dubl. Phil. Mag.
7, 905-939 (1929). |
| 18. | L. Prandtl,
"Ein Gedankenmodell zur kinetischen Theorie der festen Körper,"
ZAMM
8 (2), 85-106 (1928). |
| 19. | A. A. Burov,
"Small Sigma and Problems with Moduli,"
Kvant,
No. 1, 36-38 (2012). |
|
| Received |
10 December 2014 |
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