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The Electromagnetic Three-Body Problem With Radiation Terms Existence-Uniqueness of Periodic Orbit (II)

Yıl 2020, Cilt: 3 Sayı: 3, 137 - 159, 30.09.2020

Öz

The primary goal of the present paper is to prove an existence-uniqueness of periodic solution of the equations of motion for the 3-body problem of classical electrodynamics. The equations of motion were derived in a recent paper of the author. Particular case of this problem is the He-atom – the simplest multi-electronic
atom. We have applied our previous results to 3-body problem introducing radiation terms and in this manner we have obtained a system of 12 equations of motion. We have proved that three equations are a consequence of the first 9 ones, so that we consider 9 equations for 9 unknown functions. We introduce a suitable operator in a specific function space and formulate conditions for the existence-uniqueness of fixed point of this operator that is a periodic solution of the 3-body equations of motion. Finally, we verify the conditions obtained for the He-atom

Kaynakça

  • [1] V.G. Angelov, Fixed point theorem in uniform spaces and applications, Czechoslovak Math. J., vol. 37 (112), (1987), 19-33.
  • [2] V.G. Angelov, The N-body problem in classical electrodynamics, Physics Essays, vol. 6, No.2, (1993), 204-211.
  • [3] V.G. Angelov, Escape trajectories of J.L. Synge equations, J. Nonlinear Analysis RWA, vol. 1, (2000), 189-204.
  • [4] 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.
  • [5] V.G. Angelov, On the original Dirac equations with radiation term, Libertas Mathematica (Texas), vol. 31, (2011), 57-86.
  • [6] V.G. Angelov, A Method for Analysis of Transmission Lines Terminated by Nonlinear Loads, Nova Science, New York, 2014.
  • [7] 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, 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, The electromagnetic three-body problem with radiation terms – derivation of equations of motion (I), Results of Nonlinear Analysis, vol. 3 (2020), 45-58.
  • [11] R.D. Driver, A functional-differential systems of neutral type arising in a two-body problem of classical electrodynamics, Int. Symposium on Non-linear Differential Equations and Nonlinear Mechanics, Academic Press, (1963), 474-484.
  • [12] L.E. Elzgolz, A note on branching and vanishing of solution for equations with deviating arguments, Proceedings of the Seminar on the Theory of Differential Equations with Deviating Arguments, vol. 5, (1967), 242-245. (in Russian).
  • [13] J.L. Kelley, General Topology, Van Nostrand, 1955.
  • [14] W. Pauli, Relativitaetstheorie,Encyklopedie der Mathematischen Wissenschaften, Band. 5, Heft 4, Art. 19, (1921).
  • [15] L. Schwartz, Theorie des Distributions, Hermann & Cie, Paris, 1950/51.
  • [16] S.L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics, Moscow, 1950.
  • [17] A. Sommerfeld, Atomic Structure and Spectral Lines. London, Mathuen and Co., (1934).
  • [18] L. Synge, On the electromagnetic two-body problem,Proc.Roy. Soc. (London) A177, (1940), 118-139.
Yıl 2020, Cilt: 3 Sayı: 3, 137 - 159, 30.09.2020

Öz

Kaynakça

  • [1] V.G. Angelov, Fixed point theorem in uniform spaces and applications, Czechoslovak Math. J., vol. 37 (112), (1987), 19-33.
  • [2] V.G. Angelov, The N-body problem in classical electrodynamics, Physics Essays, vol. 6, No.2, (1993), 204-211.
  • [3] V.G. Angelov, Escape trajectories of J.L. Synge equations, J. Nonlinear Analysis RWA, vol. 1, (2000), 189-204.
  • [4] 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.
  • [5] V.G. Angelov, On the original Dirac equations with radiation term, Libertas Mathematica (Texas), vol. 31, (2011), 57-86.
  • [6] V.G. Angelov, A Method for Analysis of Transmission Lines Terminated by Nonlinear Loads, Nova Science, New York, 2014.
  • [7] 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, 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, The electromagnetic three-body problem with radiation terms – derivation of equations of motion (I), Results of Nonlinear Analysis, vol. 3 (2020), 45-58.
  • [11] R.D. Driver, A functional-differential systems of neutral type arising in a two-body problem of classical electrodynamics, Int. Symposium on Non-linear Differential Equations and Nonlinear Mechanics, Academic Press, (1963), 474-484.
  • [12] L.E. Elzgolz, A note on branching and vanishing of solution for equations with deviating arguments, Proceedings of the Seminar on the Theory of Differential Equations with Deviating Arguments, vol. 5, (1967), 242-245. (in Russian).
  • [13] J.L. Kelley, General Topology, Van Nostrand, 1955.
  • [14] W. Pauli, Relativitaetstheorie,Encyklopedie der Mathematischen Wissenschaften, Band. 5, Heft 4, Art. 19, (1921).
  • [15] L. Schwartz, Theorie des Distributions, Hermann & Cie, Paris, 1950/51.
  • [16] S.L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics, Moscow, 1950.
  • [17] A. Sommerfeld, Atomic Structure and Spectral Lines. London, Mathuen and Co., (1934).
  • [18] L. Synge, On the electromagnetic two-body problem,Proc.Roy. Soc. (London) A177, (1940), 118-139.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Vasil Angelov

Yayımlanma Tarihi 30 Eylül 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 3

Kaynak Göster

APA Angelov, V. (2020). The Electromagnetic Three-Body Problem With Radiation Terms Existence-Uniqueness of Periodic Orbit (II). Results in Nonlinear Analysis, 3(3), 137-159.
AMA Angelov V. The Electromagnetic Three-Body Problem With Radiation Terms Existence-Uniqueness of Periodic Orbit (II). RNA. Eylül 2020;3(3):137-159.
Chicago Angelov, Vasil. “The Electromagnetic Three-Body Problem With Radiation Terms Existence-Uniqueness of Periodic Orbit (II)”. Results in Nonlinear Analysis 3, sy. 3 (Eylül 2020): 137-59.
EndNote Angelov V (01 Eylül 2020) The Electromagnetic Three-Body Problem With Radiation Terms Existence-Uniqueness of Periodic Orbit (II). Results in Nonlinear Analysis 3 3 137–159.
IEEE V. Angelov, “The Electromagnetic Three-Body Problem With Radiation Terms Existence-Uniqueness of Periodic Orbit (II)”, RNA, c. 3, sy. 3, ss. 137–159, 2020.
ISNAD Angelov, Vasil. “The Electromagnetic Three-Body Problem With Radiation Terms Existence-Uniqueness of Periodic Orbit (II)”. Results in Nonlinear Analysis 3/3 (Eylül 2020), 137-159.
JAMA Angelov V. The Electromagnetic Three-Body Problem With Radiation Terms Existence-Uniqueness of Periodic Orbit (II). RNA. 2020;3:137–159.
MLA Angelov, Vasil. “The Electromagnetic Three-Body Problem With Radiation Terms Existence-Uniqueness of Periodic Orbit (II)”. Results in Nonlinear Analysis, c. 3, sy. 3, 2020, ss. 137-59.
Vancouver Angelov V. The Electromagnetic Three-Body Problem With Radiation Terms Existence-Uniqueness of Periodic Orbit (II). RNA. 2020;3(3):137-59.