 | | 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
|
| In English (Mech. Solids): | | 4760 |
|
| << 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 >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English