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Year 2020, Volume: 3 Issue: 2, 45 - 58, 30.06.2020

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References

  • [1] V. G. Angelov, The N-body problem in classical electrodynamics, Physics Essays, vol. 6, No.2, 1993, 204-211.
  • [2] V. G. Angelov, J. M. Soriano, Uniqueness of escape trajectories for N-body problem of classical electrodynamics, Math. Sci. Res. J., vol. 8, No.6, 2004, 184-195.
  • [3] V. G. Angelov, On the Synge equations in a three-dimensional two-body problem of classical electrodynamics, J. Math. Anal. Appl., vol. 151, No.2, 1990, 488–511.
  • [4] V.G. Angelov, Escape trajectories of J. L. Synge equations, J. Nonlinear Analysis RWA, vol. 1, 2000, 189–204.
  • [5] V. G. Angelov, Plane orbits for Synge’s electromagnetic two-body problem (I), Seminar on Fixed Point Theory, Cluj-Napoca, vol. 3, 2002, 3–12.
  • [6] V. G. Angelov, Plane orbits for Synge’s electromagnetic two-body problem – small perturbed circle motions (II), Fixed Point Theory, vol. 6, No.2, 2005, 231–245.
  • [7] V. G. Angelov, Two-body problem of classical electrodynamics with radiation terms - Derivation of Equations (I). Inter- national Journal of Theoretical and Mathematical Physics, vol. 5, No.5, 2015, 119-135.
  • [8] 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.
  • [9] V. G. Angelov, Two-body problem of classical electrodynamics with radiation terms - Energy Estimation (III). International Journal of Theoretical and Mathematical Physics, vol. 6, No.2, 2016, 78–85.
  • [10] V. G. Angelov, On the original Dirac equations with radiation term, Libertas Mathematica (Texas), vol. 31, 2011, 57-86.
  • [11] G. Bauer, D.-A. Deckert, and D. Durr, 2012, On the existence of dynamics in Wheeler-Feynman electromagnetism, Journal of Applied Mathematics and Physics, 64 (4), 1087-1124.
  • [12] D.-A. Deckert and G. Hinrichs, 2015, Electrodynamic two-body problem for prescribing initial date on the straight line, [Online]. Available: http://arxiv.org/abs/1507.04991.
  • [13] R. D. Driver, A two-body problem of classical electrodynamics; one-dimensional case, Annals of Physics (N.Y.), vol. 21, 1963, 122-142.
  • [14] R. D. Driver, A neutral system with state-dependent delay, J. Diff. Equations, vol. 54, No.1, 1984, 73–86.
  • [15] A. D. Myshkis, L. E. Elsgoltz, State and problems of the theory of differential equations with deviating arguments, Uspekhi Mat. Nauk, vol. 22, No.2 (134), 1967, 21–57 (in Russian).
  • [16] A. D. Myshkis, On some problems of the theory of differential equations with deviating arguments, Uspekhi Mat. Nauk, vol. 32, No.2 (134), 1977 (in Russian).
  • [17] W. Pauli, Relativitaetstheorie. Encyklopedie der Mathematischen Wissenschaften, Band. 5, Heft 4, Art. 19, 1921.
  • [18] R. W. Pohl, Optik und Atomphysik, Springer Verlag, 1963.
  • [19] J. L. Synge, On the electromagnetic two-body problem, Proc. Roy. Soc. (London), A177, 1940, 118–139.
  • [20] A. Sommerfeld, Atomic Structure and Spectral Lines, London, Mathuen and Co., 1934.

The Electromagnetic Three-Body Problem With Radiation Terms - Derivation of Equations of Motion (I)

Year 2020, Volume: 3 Issue: 2, 45 - 58, 30.06.2020

Abstract

The primary purpose of the present paper is to continue the previous investigations of the author and apply the technique from the two-body problem of classical electrodynamics to the three-body problem. We derive equations of motion with radiation terms which are neutral type nonlinear differential equations with state-dependent delays. The derivation approach is analogous to that of the two body-problem, which allows a unified consideration of the problem for any number of bodies. In the next paper, we prove the existence of periodic solution of the three-body problem and in such a way the Bohr-Sommerfeld postulate for stationary states is confirmed.

References

  • [1] V. G. Angelov, The N-body problem in classical electrodynamics, Physics Essays, vol. 6, No.2, 1993, 204-211.
  • [2] V. G. Angelov, J. M. Soriano, Uniqueness of escape trajectories for N-body problem of classical electrodynamics, Math. Sci. Res. J., vol. 8, No.6, 2004, 184-195.
  • [3] V. G. Angelov, On the Synge equations in a three-dimensional two-body problem of classical electrodynamics, J. Math. Anal. Appl., vol. 151, No.2, 1990, 488–511.
  • [4] V.G. Angelov, Escape trajectories of J. L. Synge equations, J. Nonlinear Analysis RWA, vol. 1, 2000, 189–204.
  • [5] V. G. Angelov, Plane orbits for Synge’s electromagnetic two-body problem (I), Seminar on Fixed Point Theory, Cluj-Napoca, vol. 3, 2002, 3–12.
  • [6] V. G. Angelov, Plane orbits for Synge’s electromagnetic two-body problem – small perturbed circle motions (II), Fixed Point Theory, vol. 6, No.2, 2005, 231–245.
  • [7] V. G. Angelov, Two-body problem of classical electrodynamics with radiation terms - Derivation of Equations (I). Inter- national Journal of Theoretical and Mathematical Physics, vol. 5, No.5, 2015, 119-135.
  • [8] 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.
  • [9] V. G. Angelov, Two-body problem of classical electrodynamics with radiation terms - Energy Estimation (III). International Journal of Theoretical and Mathematical Physics, vol. 6, No.2, 2016, 78–85.
  • [10] V. G. Angelov, On the original Dirac equations with radiation term, Libertas Mathematica (Texas), vol. 31, 2011, 57-86.
  • [11] G. Bauer, D.-A. Deckert, and D. Durr, 2012, On the existence of dynamics in Wheeler-Feynman electromagnetism, Journal of Applied Mathematics and Physics, 64 (4), 1087-1124.
  • [12] D.-A. Deckert and G. Hinrichs, 2015, Electrodynamic two-body problem for prescribing initial date on the straight line, [Online]. Available: http://arxiv.org/abs/1507.04991.
  • [13] R. D. Driver, A two-body problem of classical electrodynamics; one-dimensional case, Annals of Physics (N.Y.), vol. 21, 1963, 122-142.
  • [14] R. D. Driver, A neutral system with state-dependent delay, J. Diff. Equations, vol. 54, No.1, 1984, 73–86.
  • [15] A. D. Myshkis, L. E. Elsgoltz, State and problems of the theory of differential equations with deviating arguments, Uspekhi Mat. Nauk, vol. 22, No.2 (134), 1967, 21–57 (in Russian).
  • [16] A. D. Myshkis, On some problems of the theory of differential equations with deviating arguments, Uspekhi Mat. Nauk, vol. 32, No.2 (134), 1977 (in Russian).
  • [17] W. Pauli, Relativitaetstheorie. Encyklopedie der Mathematischen Wissenschaften, Band. 5, Heft 4, Art. 19, 1921.
  • [18] R. W. Pohl, Optik und Atomphysik, Springer Verlag, 1963.
  • [19] J. L. Synge, On the electromagnetic two-body problem, Proc. Roy. Soc. (London), A177, 1940, 118–139.
  • [20] A. Sommerfeld, Atomic Structure and Spectral Lines, London, Mathuen and Co., 1934.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Vasil Angelov 0000-0002-9815-9970

Publication Date June 30, 2020
Published in Issue Year 2020 Volume: 3 Issue: 2

Cite

APA Angelov, V. (2020). The Electromagnetic Three-Body Problem With Radiation Terms - Derivation of Equations of Motion (I). Results in Nonlinear Analysis, 3(2), 45-58.
AMA Angelov V. The Electromagnetic Three-Body Problem With Radiation Terms - Derivation of Equations of Motion (I). RNA. June 2020;3(2):45-58.
Chicago Angelov, Vasil. “The Electromagnetic Three-Body Problem With Radiation Terms - Derivation of Equations of Motion (I)”. Results in Nonlinear Analysis 3, no. 2 (June 2020): 45-58.
EndNote Angelov V (June 1, 2020) The Electromagnetic Three-Body Problem With Radiation Terms - Derivation of Equations of Motion (I). Results in Nonlinear Analysis 3 2 45–58.
IEEE V. Angelov, “The Electromagnetic Three-Body Problem With Radiation Terms - Derivation of Equations of Motion (I)”, RNA, vol. 3, no. 2, pp. 45–58, 2020.
ISNAD Angelov, Vasil. “The Electromagnetic Three-Body Problem With Radiation Terms - Derivation of Equations of Motion (I)”. Results in Nonlinear Analysis 3/2 (June 2020), 45-58.
JAMA Angelov V. The Electromagnetic Three-Body Problem With Radiation Terms - Derivation of Equations of Motion (I). RNA. 2020;3:45–58.
MLA Angelov, Vasil. “The Electromagnetic Three-Body Problem With Radiation Terms - Derivation of Equations of Motion (I)”. Results in Nonlinear Analysis, vol. 3, no. 2, 2020, pp. 45-58.
Vancouver Angelov V. The Electromagnetic Three-Body Problem With Radiation Terms - Derivation of Equations of Motion (I). RNA. 2020;3(2):45-58.