A possibility of levitation of a body carrying a point electrical charge in the field of a fixed point charge of the same sign is shown. Stabilization of an unstable equilibrium, when gravity is compensated by Coulomb’s force, is realized using gyroscopic forces generated due to the rotation of the body. A finite range of angular velocity corresponds to conservative stability of the levitating body. It is shown that dissipative and circulation forces introduced into consideration simultaneously can improve the stability of the system to asymptotic. Dependence of the domain of attraction of stable equilibrium on parameters of the system is studied numerically.
Issue Section:
Research Papers
1.
Earnshaw
, S.
, 1842, “On the Nature of the Molecular Forces Which Regulate the Constitution of the Luminiferous Ether
,” Trans. Cambridge Philos. Soc.
0371-5779, 116
, pp. 97
–112
.2.
Martynenko
, Y. G.
, 1996, “On Levitation of Bodies in Force Fields
,” Soros Educational Journal
, 3
, pp. 82
–86
, in Russian.3.
Merkin
, D. R.
, 1974, Gyroscopic Systems
, Nauka
, Moscow
, in Russian.4.
Hones
, E. W.
, and Hones
, W. G.
, 1995, U.S. Patent No. 5,404,062.5.
Genta
, G.
, Delprete
, C.
, and Rondano
, B.
, 1999, “Gyroscopic Stabilization of Passive Magnetic Levitation
,” Meccanica
0025-6455, 34
, pp. 411
–424
.6.
Jones
, T. B.
, Washizu
, M.
, and Gans
, R.
, 1997, “Simple Theory for the Levitron
,” J. Appl. Phys.
0021-8979, 82
(2
), pp. 883
–888
.7.
Vesselitsky
, I. V.
, Voronkov
, V. S.
, Denisov
, G. G.
, and Linkov
, R. V.
, 2005, “Spin Stabilization of Mobile Magnet in the Field of the Fixed Magnet
,” JTF
, 75
(3
), pp. 88
–93
, in Russian.8.
Bronstein
, I. N.
, and Semendyayev
, K. A.
, 1986, Manual of Mathematics
, Nauka
, Moscow
, in Russian.9.
Neymark
, Y. I.
, 1978, Dynamic Systems and Controlled Processes
, Nauka
, Moscow
, in Russian.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.