| | 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
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In English (Mech. Solids): | | 4760 |
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Yu. M. Urman, "Invariant representation of the potential interaction between a rigid body with nonuniform electromagnetic field," Mech. Solids. 40 (1), 8-13 (2005) |
Year |
2005 |
Volume |
40 |
Number |
1 |
Pages |
8-13 |
Title |
Invariant representation of the potential interaction between a rigid body with nonuniform electromagnetic field |
Author(s) |
Yu. M. Urman (Nizhni Novgorod) |
Abstract |
Problems of motion of rigid bodies in nonuniform force fields of various
physical nature are characterized by a much more complex structure of
body-field interaction as compared with the classical problem of motion of
a rigid body with a fixed point in the uniform gravity field. In such
problems, it is essential to take into account the torques described by
tensor interaction. An even more complex interaction is observed in the
case of contactless suspension with field sources surrounding the rotor from
all sides close to its surface.
In view of this, it is desirable to have a model of the body-field
interaction that could be conveniently used in investigations. Moreover,
since the complex structure of the torques practically prevents an exact
analytic investigation of all motions of a body in the force field, the
said model should also be convenient for finding and studying approximate
equations governing nonstationary motions of a body.
Finding the force function for the interaction of a body of an arbitrary
shape with a field is usually a very difficult task, since one has to solve
a boundary value problem of mathematical physics in a domain the boundary of which
has a complex structure. In this paper, it is shown how, using the
technique of irreducible tensors, one can immediately obtain an invariant
representation of the force function for the body-field interaction without
solving the boundary value problem.
This method is demonstrated for a body of an arbitrary shape with
nonhomogeneous magnetic or electric properties interacting with a
nonuniform electric or magnetic field. The general method is justified by
examples for which specific calculations can be done. In the case of small
dielectric or magnetic susceptibility of the rigid body, an analytical
expression is obtained for the force function and the torques due to the
interaction between various field harmonics and the body. In the case of an
arbitrary dielectric susceptibility, the force function is obtained for a
spherical body in a nonuniform field and an elliptic body in a uniform
field. |
References |
1. | G. G. Denisov and Yu. M. Urman, "Precession motions of a rigid
body subjected to torques that have a force function," Izv. AN SSSR. MTT
[Mechanics of Solids], No. 6, pp. 5-14, 1975. |
2. | Yu. M. Urman, "An invariant expansion of the force function for
mutual attraction of a system of bodies," Astron. Zh., Vol. 66, No. 5,
pp. 1081-1092, 1989. |
3. | Yu. M. Urman, "Addition theorems for tensor spherical wave
functions," Zh. Tekhn. Fiz., Vol. 51, No. 3, pp. 457-462, 1981. |
4. | Yu. M. Urman, "Application of the method of irreducible tensors in
problems of evolutionary motion of a rigid body with a fixed point," Izv.
AN. MTT [Mechanics of Solids], No. 4, pp. 10-20, 1997. |
5. | A. I. Vorob'ev and Yu. M. Urman, "Forces and perturbation torques
acting on the rotor of a cryogenic gyroscope," Izv. AN SSSR. MTT
[Mechanics of Solids], No. 2, pp. 15-23, 1984. |
6. | D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum
Theory of the Angular Momentum [in Russian], Nauka, Moscow, 1975. |
7. | L. D. Landau and E. M. Lifshitz, Theoretical Physics. Volume 8.
Electrodynamics of Continuous Media [in Russian], Nauka, Moscow, 1982. |
8. | M. L. Levin and R. Z. Muratov, "Dielectric ellipsoid in a
nonuniform static field," Zh. Tekhn. Fiz., Vol. 47, No. 12,
pp. 2464-2471, 1977. |
|
Received |
26 November 2002 |
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