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 Issues2002-2pp.28-38

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 37, Issue 2 / 2002 | Next article >>
V. I. Kuvykin and Yu. G. Martynenko, "Motion of a conducting rigid body in a nonuniform magnetic field," Mech. Solids. 37 (2), 28-38 (2002)
Year 2002 Volume 37 Number 2 Pages 28-38
Title Motion of a conducting rigid body in a nonuniform magnetic field
Author(s) V. I. Kuvykin (Moscow)
Yu. G. Martynenko (Moscow)
Abstract A conducting rigid body of an arbitrary shape placed in a prescribed nonuniform magnetic field is considered. An asymptotic relation is determined for eddy currents inside the body in the case of slow motions characterized by large depth of penetration of the magnetic field into the conductor. Ponderomotive forces and their moments are calculated in the first approximation with respect to the small parameter of the problem. The structure of the differential equations governing the motion of the center of mass and the attitude motion of the body is analyzed. Dynamic effects caused by coupling of translational and rotational motions of a rigid body in a nonuniform magnetic field are discussed.

Problems of the force action of a magnetic field on a conducting body are encountered in various fields of modern engineering, for example, when analyzing the effects of the magnetic field on the dynamics of bodies in space, studying the levitation of bodies in contactless suspensions, investigating the operation of magnetic dampers, designing magnetic catapults or a train on a magnetic suspension. At the present time, the motion of a conducting body in a uniform magnetic field has been thoroughly studied [1-4]. In this case, the net ponderomotive force vanishes and the problem is reduced to the analysis of only the attitude motion of the body. For a conducting ball performing the motion of the type of regular precession, differential equations governing the attitude motion of a rapidly spun ball in a nonuniform magnetic field have been derived. For a spherically symmetric body, the equations of electrodynamics can be solved by the method of separation of variables [5].

The authors of the present paper do not know works devoted to the analysis of an arbitrary motion of a (nonspherical) rigid body in a nonuniform magnetic field. In this case, the net ponderomotive force does not vanish and its magnitude in the general case depends on the orientation of the body in the magnetic field, which leads to coupling of the translational and rotational motions of the body.

The difficulty of the analysis of the dynamics of a rigid body in a magnetic field is due to the necessity to solve the equations of electrodynamics simultaneously with the equations of dynamics of a rigid body. For specific prescribed classes of motion of a rigid body, one can construct simplified mathematical models by using asymptotic methods of separating fast and slow variables [2]. In the present paper, this approach is utilized to construct a simplified mathematical model governing the behavior of a rigid body in a nonuniform magnetic field for slow motions relative to the field.
References
1.  V. V. Beletskii and A. A. Khentov, Rotational Motion of a Magnetized Satellite [in Russian], Nauka, Moscow, 1985.
2.  Yu. G. Martynenko, Motion of a Rigid Body in Electric and Magnetic Fields [in Russian], Nauka, Moscow,1988.
3.  V. I. Kuvykin and Yu. G. Martynenko, "An estimate of the braking torque acting on an electrodynamic damper for a contactless suspension," Elektrichestvo, No. 11, pp. 30-33, 1994.
4.  B. I. Rabinovich, V. G. Lebedev, and A. I. Mytarev, Eddy Processes in Dynamics of a Rigid Body [in Russian], Nauka, Moscow, 1992.
5.  R. V. Lin'kov and Yu. M. Urman, "Force action on a conducting ball moving in a magnetic field," Zh. Tekhn. Fiziki, Vol. 47, No. 4, pp. 716-723, 1977.
6.  L. D. Landau and E. M. Lifshits, Electrodynamics of Continuum [in Russian], Nauka, Moscow, 1982.
7.  A. B. Vasil'eva and V. F. Butuzov, Asymptotic Expansions of Solutions of Singularly Perturbed Equations [in Russian], Nauka, Moscow, 1973.
8.  P. K. Suetin, Classical Orthogonal Polynomials [in Russian], Nauka, Moscow, 1979.
9.  N. E. Zhukovskii, "On the motion of a rigid body having cavities filled with a homogeneous dropping liquid," in N. E. Zhukovskii. Collected Works [in Russian], Vol. 2, pp. 152-309, GITTL, Moscow, Leningrad, 1949.
Received 02 February 2000
<< Previous article | Volume 37, Issue 2 / 2002 | 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