 | | 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
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| Yu. M. Urman, "Method of irreducible tensors in problems of rotation of a conductive body in nonuniform magnetic fields," Mech. Solids. 36 (2), 8-15 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
2 |
Pages |
8-15 |
| Title |
Method of irreducible tensors in problems of rotation of a conductive body in nonuniform magnetic fields |
| Author(s) |
Yu. M. Urman (Nizhni Novgorod) |
| Abstract |
The ponderomotive interaction of a moving conductive body with a
nonuniform magnetic field has a significant feature that mechanical
degrees of freedom are coupled due to eddy currents. The coupling
results in a "pumping" of energy from one degree of freedom to
another. In addition, a number of destabilizing factors appear
which are unusual for the traditional interaction of a conductor with
a magnetic field. As a result, the deceleration of the body
changes to its acceleration, a repulsive force changes to an attractive
one, a "negative friction" and a nonconservative "circulatory force"
appear.
To get full understanding of the interaction between a moving conductive
body and magnetic field one should solve simultaneously the equations of
electrodynamics and mechanics. However, this problem is extremely
complicated and cannot be solved analytically in its general formulation
even for simple geometric bodies. There are a number of papers [1-3]
devoted to the solution of this problem by asymptotic methods based on
the assumption that the depth of penetration of the field into the
conductor is small or large. For spherical bodies (a ball, a spherical
shell) and some specific types of their motion, one can successfully solve
the boundary value problem in a fairly general formulation
and find the ponderomotive interaction of the body and the field.
Although it is a particular problem, the analysis of the ponderomotive
interaction allows one to reveal a number of effects
which are of interest as physical phenomena and as factors affecting
the stability of the body supported by the field. Moreover, this problem
has an independent value since the eddy currents due the motion of a
conductive body in a magnetic field (together with viscous
friction) is a widespread source of dissipative forces.
As shown in [4], the torque in general can be decomposed into the
conservative and nonconservative components. The conservative component
of the torque is generated by one scalar function, while the nonconservative
component is generated by two scalar functions depending on the magnitude
and direction of the angular momentum.
In the present paper, these functions are calculated for the case of
rotation of a conductive ball in a nonuniform magnetic field. Also, it
is shown that, as was the case for the net torque, the net force acting
on the body can be decomposed into the conservative and nonconservative
components. |
| References |
| 1. | A. N. Kobrin and Yu. G. Martynenko, "Dynamics of a conductive
rigid body in a high-frequency magnetic field," Doklady AN SSSR,
Vol. 255, No. 5, pp. 1063-1065, 1980. |
| 2. | A. N. Kobrin and Yu. G. Martynenko, "A motion of a conductive
rigid body about the mass center in a slowly varying magnetic field,"
Doklady AN SSSR, Vol. 261, No. 5, pp. 1070-1073, 1981. |
| 3. | Yu. G. Martynenko, Motion of a Rigid Body in Electrical and
Magnetic Fields [in Russian], Nauka, Moscow, 1988. |
| 4. | Yu. M. Urman, "Method of irreducible tensors in
problems of evolution motions of a rigid body with a fixed point,"
Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 10-20, 1997. |
| 5. | J. Jackson, Classical Electrodynamics [Russian translation],
Mir, Moscow, 1965. |
| 6. | Yu. M. Urman, "Irreducible tensors and their application to
the problems of rigid body motion in force fields," in Mechanics of a
Rigid Body [in Russian], Vol. 15, pp. 75-87, Naukova Dumka, Kiev, 1983. |
| 7. | D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii,
Quantum Theory of the Angular Momentum [in Russian], Nauka, Leningrad, 1975. |
| 8. | L. D. Landau and E. M. Lifshits, Theoretical Physics. Volume 8.
Electrodynamics of Continuous Media [in Russian], Nauka, Moscow, 1982. |
| 9. | R. V. Lin'kov and Yu. M. Urman, "A rotating ball in a magnetic
field," Zh. Tekhn. Fiziki, Vol. 43, No. 12, pp. 2472-2480, 1973. |
|
| Received |
22 October 1998 |
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