Spin 3-Body Problem Of Classical Electrodynamics In The 3D-Kepler Form

Authors

  • Vasil G. Angelov University of Mining and Geology ”St. I. Rilski”, Department of Mathematics and Informatics, 1700 Sofia, Bulgaria

Keywords:

spin functions, classical electrodynamics, three-body problem, periodic solutions, fixed point method

Abstract

In the present paper we prove the existence of spin functions for 3-body problem of classical electrodynamics. It is a direct continuation of a previous paper in which we proved the existence and uniqueness of a periodic solution to the same problem in 3D Kepler form. To prove the existence of periodic spin functions we use fixed point method for operator equations.

References

[1] Angelov V.G., The electromagnetic three-body problem with radiation terms – derivation of equations of motion (I), Results in Nonlinear Analysis, vol. 3, No.2, (2020), 45-58.

[2] Angelov V.G., The electromagnetic three-body problem with radiation terms – existence-uniqueness of periodic orbit (II), Results in Nonlinear Analysis, vol. 3, No.3, (2020), 137- 158.

[3] Angelov V.G., Spin three-body problem of classical electrodynamics with radiation terms (I) - derivation of spin equations. Results in Nonlinear Analysis, vol. 4, No.1, (2021), 1-20. (ISSN 2636-7556).

[4] Angelov V.G., Three-Body 3D-Kepler Electromagnetic Problem—Existence of Periodic solutions. Applied Math. (2024), vol. 4, 612–640. https://doi.org/10.3390/appliedmath4020034.

[5] Pauli W., Relativitatstheorie. Encyklopedie der mathematischen Wissenschaften, Band. 5, Heft 4, Art. 19, 1921.

[6] Herglotz G. Gottingen Nachrichten, math.-naturw. KL, (1904), p. 549.

[7] Sommerfeld A., Annalen der Physik, Bd 33, (1910), p. 665.

[8] Synge, J.L., On the electromagnetic two-body problem, Proc. Roy. Soc. (London), A177, 1940, 118-139.

[9] Krasnoselskii M.A., Shifting operator along trajectories of differential equations. Nauka, Moscow, 1966 (in Russian).

[10] Corben H.C., and P. Stehle, Classical Mechanics. New York, London: J. Wiley and Sons, 1960.

[11] Corben H.C., Spin in classical and quantum theory, Physical Review, vol. 121, No.6, 1961, 1833-1839.

[12] Mathisson M., Neue mechanik materieller systeme, Acta Physica Polonica, vol. 6, 1937, 163-227.

[13] Nyborg P., Macroscopic motion of classical spinning particles, Nuovo Cimento, vol. 26, No.4, 1962, 821-830.

[14] Schild A., and J. A. Schlosser, Fokker action principle for particles with charge, spin, and magnetic moment. J. Mathematical Physics, vol. 6, No.8, 1965, 1299-1306.

[15] Schiller R., Quasi-classical theory of the spinning electron. Physical Review, vol. 125, No.3, 1962, 1116-1123.

[16] Weyssenhoff J., and A. Raabe, Relativistic dynamics of spin-fluids and spin-particles. Acta Physica Polonica, vol. 9, No.1, 1947, 7-18.

Downloads

Published

2024-06-17

Issue

Section

Articles