Spin Three-Body Problem of Classical Electrodynamics with Radiation Terms (I) Derivation of Spin Equations

Öz

In the present paper, the spin equations for the three-body problem of classical electrodynamics are introduced. They should be considered jointly with 3-body equations of motion derived in a previous paper of the author. The system of spin equations is an overdetermined one. It is shown that the independent spin equations are nine in number as many as the components of the unknown spin functions. The system obtained will be solved by the fixed-point method in the next paper.

Anahtar Kelimeler

• Spin three-body problem
• Classical electrodynamics
• Spin equations

Kaynakça

1. [1] V.G. Angelov, The N-body problem of classical electrodynamics” Physics Essays, vol. 6, No.2, 1993, 204-211.
2. [2] V.G. Angelov, Two-body problem of classical electrodynamics with radiation terms – derivation of equations (I), International Journal of Theoretical and Mathematical Physics, vol. 5, 2015, 119-135.
3. [3] V.G. Angelov, Two-body problem of classical electrodynamics with radiation terms – periodic solutions (II), International Journal of Theoretical and Mathematical Physics, vol. 6, No.1, 2016, 1-25.
4. [4] V.G. Angelov, Spin two- body problem of classical electrodynamics with radiation terms (I) – derivation of spin equations, International Journal of Theoretical and Mathematical Physics, vol. 7, No.5, 2017, 132-154.
5. [5] V. G. Angelov, 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.
6. [6] V.G. Angelov, 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.
7. [7] A.O. Barut, C. Onem, and N. Unal, The Classical Relativistic Two-Body Problem with Spin and Self-Interactions, Int. Centre for Theoretical Physics, Trieste, 1989, 1-19.
8. [8] G. Bauer, D.-A. Deckert, D. Durr, and G. Hinrichs, On irreversibility and radiation in classical electrodynamics of point particles, Journal of Statistical Physics, vol. 154, No.1-2: 610, 12 pages, 2014.

9. [9] G. Bauer, D.-A. Deckert, and D. Durr, On the existence of dynamics in Wheeler-Feynman electromagnetism, Journal of Applied Mathematics and Physics, vol. 64, No.4, 2012, 1087 -1124.
10. [10] H.C. Corben, and P. Stehle, Classical Mechanics. New York, London: J. Wiley and Sons, 1960.
11. [11] H.C. Corben, Spin in classical and quantum theory, Physical Review, vol. 121, No.6, 1961, 1833-1839.
12. [12] D.-A. Deckert, and G. Hinrichs, Electrodynamic two-body problem for prescribing initial date on the straight line, [Online], Available: http://arxiv.org/abs/1507.04991.
13. [13] D.-A. Deckert, D. Durr, and N. Vona, Delay equations of the Wheeler-Feynman type, in Proc. Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14-21, 2011, Part 3, Journal of Contemporary Mathematics. Fundamental Directions, 47: 46, 2013, 13 pages.
14. [14] J.B. Hughes, A generalized Hamiltonian dynamics for relativistic particles with spin, Nuovo Cimento, vol. 20, No.2, 1961, 89-156.
15. [15] J. De Luca, Variational electrodynamics of atoms, Progress in Electromagnetism Research, B, 1-11, July 2013.
16. [16] M. Mathisson, Neue mechanik materieller systeme, Acta Physica Polonica, vol. 6, 1937, 163-227.
17. [17] P. Nyborg, Macroscopic motion of classical spinning particles, Nuovo Cimento, vol. 26, No.4, 1962, 821-830.
18. [18] A. Schild, 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.
19. [19] R. Schiller, Quasi-classical theory of the spinning electron, Physical Review, vol. 125, No.3, 1962, 1116-1123.
20. [20] J. Weyssenhoff, and A. Raabe, Relativistic dynamics of spin-fluids and spin-particles, Acta Physica Polonica, vol. 9, No.1, 1947, 7-18.