Cybernetics And Systems Analysis logo
Editorial Board Announcements Abstracts Authors Archive
KIBERNETYKA TA SYSTEMNYI ANALIZ
International Theoretical Science Journal
-->

DOI 10.34229/KCA2522-9664.24.3.5
UDC 531.011; 004.942; 621.31; 37.036.5
S.S. Zub1, I.H. Yalovega2, V.S. Lyashko3, S.I. Lyashko4


1 Military Unit No. А7403, Ukraine

stah_z@yahoo.com

2 Simon Kuznets Kharkiv National University of Economics, Kyiv, Ukraine

yalovega.ira@gmail.com

3 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

lyashko.serg@gmail.com

4 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

Lyashko91@gmail.com

MATHEMATICAL MODEL OF MAGNET SUPERCONDUCTING SUSPENSION

Abstract. A complete study of the stability of static equilibrium in the system was carried out using the explicitly obtained function of the potential energy of the magnetic system, which consists of a superconducting ring and a magnetic dipole in a uniform gravitational field. The conditions for equilibrium were analytically found, and the stability domain was constructed. It is shown that when the found conditions are met, a static magnetic levitation in the form of a suspension takes place around the axis of the ring. The performed calculations demonstrate the stability of equilibrium in the form of a suspension based on the magnetic levitation mechanism proposed by V. Kozoriz.

Keywords: mathematical model, magnetic levitation, magnetic potential energy, stability of equilibrium, superconducting suspension, permanent magnet.


full text

REFERENCES

  1. Gibbs Ph., Geim A. Is magnetic levitation possible? 1997. URL: http://math.ucr.edu/home/baez/physics/General/Levitation/levitation.html .

  2. Thomson W. On the forces experienced by small spheres under magnetic influence; and on some of the phenomena presented by diamagnetic substances. Camb. Dublin Math. J. 1847. Vol. 2. P. 230–252. http://kirkmcd.princeton.edu/examples/EM/thomson_cdmj_2_230_47.pdf .

  3. Braunbek W. Freies Schweben diamagnetischer Korper im Magnetfeld. Z. Phys. 1939. Vol. 112. P. 764–769. https://doi.org/10.1007/BF01339980.

  4. Kozlov V.V. About the degree of instability. Prikla. Mat. i mekh. 1993. Vol. 57, Iss. 5. P. 14–19.

  5. Daniels B., Matthews P.W. Superconducting bearing. Review of Scientific Instruments. 1966. Vol. 37, Iss. 6. P. 750–753. https://doi.org/10.1063/1.1720313.

  6. Kozoriz V.V., Kolodeev I.D., Kryukov M.I. etc. On the potential well of the magnetic interaction of ideal current circuits. DAN of the USSR. Ser. А. 1976. N 3. P. 248–249.

  7. Mikhalevich V.S., Kozorez V.V., Rashkovan V.M. etc. “Magnetic potential well” - the effect of stabilization of superconducting dynamic systems [in Russian]. Kyiv: Nauk. Dumka, 1991. 335 p.

  8. Gantmakher F.R. Lectures in analytical mechanics [Russian translation]. Moscow: Mir, 1975. 262 р.

  9. Lyashko S.I., Zub S.S., Yalovega I.G., Lyashko V.S. Mathematical model of permanent magnets and superconducting coils. Cybernetics and Systems Analysis. 2022. Vol. 58, N 1. P. 77–83. https://doi.org/10.1007/s10559-022-00480-z .

  10. Zub S.S. Stable orbital motion of magnetic dipole in the field of permanent magnets. Physica D: Nonlinear Phenomena. 2014. Vol. 275. P. 67–73. https://doi.org/10.1016/j.physd.2014.02.007.

  11. Smythe W.R. Static and dynamic electricity. New York: McGraw-Hill, 1967. 623 p.

  12. Landau L.D., Lifshitz E.M. Electrodynamics of continuous media. 2nd ed. Robert Maxwell, M.C., 1984. https://doi.org/10.1016/B978-0-08-030275-1.50025-4.




© 2024 Kibernetika.org. All rights reserved.