Mechanics of Solids (about journal) 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

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2010-1pp.22-26

Archive of Issues

Total articles in the database: 12854
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8044
In English (Mech. Solids): 4810

<< Previous article | Volume 45, Issue 1 / 2010 | Next article >>
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
<< Previous article | Volume 45, Issue 1 / 2010 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100