 | | 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: | | 12882 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
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| In English (Mech. Solids): | | 4811 |
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| A.P. Blinov, "On a Toroidal Pendulum," Mech. Solids. 45 (1), 22-26 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
1 |
Pages |
22-26 |
| DOI |
10.3103/S0025654410010048 |
| Title |
On a Toroidal Pendulum |
| Author(s) |
A.P. Blinov (Timiryazev Moscow Agriculture Academy, Russian State Agricultural University, Timiryazevskaya 49, Moscow, 127550, Russia) |
| Abstract |
We consider the problem of motion of a heavy particle on the surface of a torus with horizontal axis of rotation.
On nondevelopable surfaces other than surfaces of revolution with vertical axis, the solution is known only for the surface of an elliptic paraboloid [1].
To solve the problem on the surface of a torus with horizontal axis of rotation, we use the method of reduction of equations of motion proposed in [2]. We construct the asymptotics of the general and periodic solutions and show that one can use this asymptotics when studying the motion of a heavy particle on an elliptic torus.
We obtain the stability conditions in the first approximation for the particle motion along the outer equator and the lower meridian of the torus. |
| Keywords |
surface, torus, line, particle, reduction, rotation, libration, geodesic, energy, stability |
| References |
| 1. | S. A. Chaplygin,
Complete Collection of Works,
Vols. 1-13
(Izd-vo AN SSSR, Leningrad, 1933-1935)
[in Russian]. |
| 2. | A. P. Blinov,
"On the Motion of a Mass Point on a Surface,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 23-28 (2007)
[Mech. Solids (Engl. Transl.)
42 (1), 19-23 (2007)]. |
| 3. | F. G. Tricomi,
Differential Equations
(Hafner, New York, 1961; Izd-vo Inostr. Lit., Moscow, 1962). |
| 4. | G. N. Duboshin,
Celestial Mechanics. Fundamental Problems and Methods
(Fizmatgiz, Moscow, 1963;
Translation Div., Wright-Patterson Air-Force Base, Fairborn, Ohio, 1969). |
| 5. | B. P. Demidovich,
Lectures on Mathematical Theory of Stability
(Nauka, Moscow, 1967)
[in Russian]. |
| 6. | J. K. Hale,
Oscillations in Nonlinear Systems
(McGraw Hill, New York, 1963; Mir, Moscow, 1966). |
| 7. | N. E. Zhukovskii,
"Finiteness Conditions for Integrals of the Equation d2y/dx2+py=0,"
in Complete Papers, Vol. 1
(Gostekhizdat, Moscow-Leningrad, 1948)
pp. 246-253
[in Russian]. |
| 8. | I. G. Malkin,
Several Problems of Theory of Nonlinear Oscillations
(Gostekhizdat, Moscow, 1956)
[in Russian]. |
| 9. | V. Ph. Zhuravlev and D. M. Klimov,
Applied Methods in Vibration Theory
(Nauka, Moscow, 1988)
[in Russian]. |
|
| Received |
10 April 2008 |
| Link to Fulltext |
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