 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| A.A. Zobova, "Various Friction Models in Two-Sphere Top Dynamics," Mech. Solids. 48 (2), 134-139 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
2 |
Pages |
134-139 |
| DOI |
10.3103/S0025654413020039 |
| Title |
Various Friction Models in Two-Sphere Top Dynamics |
| Author(s) |
A.A. Zobova (Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia, azobova@gmail.com) |
| Abstract |
The dynamics of a two-sphere tippe top on a rough horizontal plane is considered. The top is bounded by a nonconvex surface consisting of two spherical segments of distinct radii and a cylinder; the cylinder axis coincides with the common symmetry axis of the segments. If the top is initially placed so that its center of mass is almost in the lowest position, the symmetry axis is almost vertical, and a high angular velocity of rotation about the vertical symmetry axis is imparted to the top, then it turns upside down from its base to the leg and starts to rotate on the leg. Then the top gradually returns to the stable equilibrium. The problem of the top motion is often used to demonstrate the efficiency of various proposed friction models [1-3].
The effects arising in the two-sphere top dynamics with various dry friction models are compared in the present paper. Both analytic methods based on the theory of stability and bifurcations and numerical calculations are used. The numerical study is performed under the assumption that the supporting plane is deformable, which permits one to describe transient processes accompanied with impacts by using a single system of equations. |
| Keywords |
dry friction, dynamics of a body on a deformable plane, tippe top |
| References |
| 1. | P. Contensou,
"Couplage entre frottenment de glissement et frottenment de pivotement dans la théorie de la toupie,"
in Kreiselprobleme Gyrodynamics
(IUTAM Symp. Celerina, Berlin etc., Springer 1963; Mir, Moscow, 1967),
pp. 201-216 (60-77). |
| 2. | R. I. Leine and Ch. Gloker,
"A Set-Valued Force Law for Spatial Coulomb-Contensou Friction,"
Europ. J. Mech. A/Solids
22 (2), 193-216 (2003). |
| 3. | V. Ph. Zhuravlev and D. M. Klimov,
"On the Dynamics of the Thompson Top (Tippe Top) on the Plane with Real Dry Friction,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 157-168 (2005)
[Mech. Solids (Engl. Transl.)
40 (6), 117-127 (2005)]. |
| 4. | V. Ph. Zhuravlev,
"The Model of Dry Friction in the Problem of the Rolling of Rigid Bodies,"
Prikl. Mat. Mekh.
62 (5), 762-767 (1998)
[J. Appl. Math. Mech. (Engl. Transl.)
62 (5), 705-710 (1998)]. |
| 5. | A. V. Karapetyan,
"A Two-Parameter Friction Model,"
Prikl. Mat. Mekh.
73 (4), 515-519 (2009)
[J. Appl. Math. Mech. (Engl. Transl.)
73 (4), 367-370 (2009)]. |
| 6. | E. J. Routh,
The Advanced Part of a Treatise on the Dynamics of a System of Rigid Bodies
(MacMillanm, London, 1884). |
| 7. | A. V. Karapetyan,
Stability of Stationary Motions
(Editorial URRS, Moscow, 1998)
[in Russian]. |
| 8. | A. A. Zobova and A. V. Karapetyan,
"Analysis of the Steady Motions of the Tippe Top,"
Prikl. Mat. Mekh.
73 (6), 867-877 (2009)
[J. Appl. Math. Mech. (Engl. Transl.)
73 (6), 623-630 (2009)]. |
| 9. | A. V. Karapetyan,
"Global Qualitative Analysis of Tippe Top Dynamics,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 33-41 (2008)
[Mech. Solids (Engl. Transl.)
43 (3), 342-348 (2008)]. |
|
| Received |
08 December 2010 |
| Link to Fulltext |
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