Spin 3-Body Problem with Radiation Terms (II) - Existence of Periodic Solutions of Spin Equations

The present paper is devoted to the existence of a periodic solution of the spin equations for three-body problem of classical electrodynamics. These equations are derived in a previous paper. We present in an operator form the system in consideration and by fixed point method prove an existence of a periodic solution.

Keywords:

classical electrodynamics, spin equations spin three-body problem,

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[1] V.G. Angelov, Fixed Points in Uniform Spaces and Applications, Cluj Univesity Press, Cluj-Napoca, 2009.
[2] V.G. Angelov, The N-body problem of classical electrodynamics, Physics Essays 6, No. 2 (1993), 204-211.
[3] V.G. Angelov, Two-body problem of classical electrodynamics with radiation terms - derivation of equations (I), Interna- tional Journal of Theoretical and Mathematical Physics 5 (2015), 119-135.
[4] V.G. Angelov, Two-body problem of classical electrodynamics with radiation terms - periodic solutions (II), International Journal of Theoretical and Mathematical Physics 6 (1) (2016), 1-25.
[5] 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 7 (5) (2017), 132-154.
[6] V.G. Angelov, The electromagnetic three-body problem with radiation terms - derivation of equations of motion (I), Results in Nonlinear Analysis 3, No. 2 (2020), 45-58.
[7] V.G. Angelov, The electromagnetic three-body problem with radiation terms - derivation of equations of motion (II), Results in Nonlinear Analysis 3, No. 3 (2020), 137-158.
[8] V G. Angelov, Spin three-body problem of classical electrodynamics with radiation terms (I) - derivation of spin equations, Results in Nonlinear Analysis 4, No. 1 (2021), 1-20. (ISSN 2636-7556)
[9] A.O. Barut, C. Onem and N. Unal, The classical relativistic two-body problem with spin and self-interactions, International Centre for Theoretical Physics, Trieste (1989), 1-19.
[10] G. Bauer, D.-A. Deckert, D. Durr, On the existence of dynamics in Wheeler-Feynman electromagnetism, Journal of Applied Mathematics and Physics 64 (4) (2012), 1087-1124.
[11] G. Bauer, D.-A. Deckert, D. Durr, G. Hinrichs, On irreversibility and radiation in classical electrodynamics of point particles, Journal of Statistical Physics 154 (1) (2014), 610-622.
[12] H.C. Corben and P. Stehle, Classical Mechanics, J. Wiley and Sons, New York, London, 1960.
[13] H.C. Corben, Spin in classical and quantum theory, Physical Review 121 (6), 1833-1839.
[14] 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.
[15] D.-A. Deckert, D. Durr and N. Vona, Delay equations of the Wheeler-Feynman type, 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.
[16] J.B. Hughes, Generalized Hamiltonian dynamics for relativistic particles with spin, Nuovo Cimento 20, No. 2 (1961), 89-156.
[17] J. De Luca, Variational electrodynamics of atoms, Progress in Electromagnetism Research, B, 1-11, July 2013.
[18] M.A. Krasnoselskii, Shifting operator along trajectories of differential equations, Nauka, Moscow, 1966 (in Russian). [19] M. Mathisson, Neue mechanik materieller systeme, Acta Physica Polonica 6 (1937), 163-227.
[20] P. Nyborg, Macroscopic motion of classical spinning particles, Nuovo Cimento 26, No. 4 (1962), 821-830.
[21] W. Pauli, Relativitätstheorie, Encyklopädie der mathematischen Wissenschaften, Band. 5, Heft 4, Art. 19 (1921).
[22] A. Schild and J.A. Schlosser, Fokker action principle for particles with charge, spin, and magnetic moment, J. Mathematical Physics 6, No. 8 (1965), 1299-1306.
[23] R. Schiller, Quasi-classical theory of the spinning electron, Physical Review 125, No. 3 (1962), 1116-1123.
[24] J.L. Synge, On the electromagnetic two-body problem, Proc. Roy. Soc. (London) A177 (1940), 118-139.
[25] J. Weyssenhoff and A. Raabe, Relativistic dynamics of spin-?uids and spin-particles, Acta Physica Polonica, 9, No. 1 (1947), 7-18.