Welcome to Francis Academic Press
Login | Register

The Frontiers of Society, Science and Technology, 2021, 3(2); doi: 10.25236/FSST.2021.030214.

Chaotic system and special cases in restricted three-body problem

Author(s)

Jiacheng Wang1, Jhon Tu2, Yicheng Zhao3

Corresponding Author:
Jiacheng Wang
Affiliation(s)

1Shandong Experimental High School, Jinan, 250001, China.

2United World College of Changshu, Changshu, 215501, China.

3Fuzhou No.1 High School, Fuzhou, 350001, China.

Abstract

This paper mainly analyzes the chaotic systems behind the three-body problem, establishing the relationship between initial parameters of the three stars and the degree of chaos, classifying and comparing the Lagrangian (some or famous) points with computer simulation and mathematical demonstration. Moreover, this paper also presents the analysis for the special cases of three-body systems in two-dimensional plane with stabilized patterns of every specific solution with computer simulation and theoretical demonstrations.

Keywords

Chaotic system, Lagrangian points, Specific solution, Two-dimensional restricted, Three-body problem

Cite This Paper

Jiacheng Wang, Jhon Tu, Yicheng Zhao. Chaotic system and special cases in restricted three-body problem. The Frontiers of Society, Science and Technology (2021) Vol. 3, Issue 2: 97-112. https://doi.org/10.25236/FSST.2021.030214.

References

[1] Anosova, Z. P., Computer simulations in the general three-body problem - The theoretical bases of the studies, Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958). [1990]. vol. 48, no. 4, 1990, p. 357-373.

[2] Z.E. Musielak and B. Quarles. The three-body problem, Reports on Progress in Physics arXiv:1508.02312v1 [astro-ph.EP] 10 Aug 2015

[3] Jules Henri Poincaré, New Methods of Celestial Mechanics[1892–1899]

[4] Szebehely V., Theory of orbits: the restricted three body problem, Academic Press. [1967]. p. 126-230

[5] Anosova, Z. P., Computer simulations in the general three-body problem - The theoretical bases of the studies, Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), [1990]. vol. 48, no. 4, 1990, p. 357-373.

[6] Edward Norton Lorenz, Deterministic Nonperiodic Flow, Journal of the Atmospheric Sciences. [1963]. Vol.20, p.130-141.

[7] Lagrange J L,. Essai sur le probleme des trois orps -uvres, [1772]. vol. 6 p 273

[8] Kei Yamada and Hideki Asada, 20th workshop on General Relativity and Gravitation in Japan(JGRG20). [2001]. p. 440-443. 

[9] C. Simó, Dynamical properties of the figure eight solution of the three-body problem. Preprint. (Departament de Matematica `Aplicada i Analisi. Universitat de Barcelona). Mexico oct.2003. vol. 49, no.5 

[10] A. Chenciner and R. Montgomery, A remarkable periodic solution of the three-body problem in the case of equal masses, Ann. of Math., November. [2000]. vol. 152, p. 881-901

[11] Euler, Leonhard, "De motu rectilineo trium corporum se mutuo attrahentium" (1767). Euler Archive - All Works. 327.

[12] Matthew Beckler. Behavior of Satellite Objects in the Earth-Moon Lagrange Points. arXiv:1912.01894v1 [astro-ph.EP] 4 Dec 2019.