Geometric Characterizations for Variational Minimization Solutions of the 3-Body Problem

Acta Mathematica Sinica, English Series

Volumn 16, Issue 4, 2000, Pages 579-592

  Long, Yiming ^a   Zhang, Shiqing ^b  

^a NANKAI UNIVERSITY   (China)

^b CHONGQING UNIVERSITY   (China)

Author keywords

3 body problem; Equilateral triangle circular solution; Restricted 3 body problem; Variational minimization

Indexed keywords

EID: 0347935884     PISSN: 14398516     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101140000007     Document Type: Article

References (18)

1. P Rabinowitz. Periodic solutions of Hamiltonian systems. Comm Pure Appl Math, 1978, 31: 157-184
2. A Ambrosetti, V Coti Zelati. Periodic Solutions of Singular Lagrangian Systems. Birkhäuser, Basel, 1993
3. G F Dell'Antonio. Classical solutions of a perturbed N-body system. In Topological Nonlinear Analysis II M Matzeu and A Vignoli ed Birkhäuser, 1997, 1-80
4. U Bessi, V Coti Zelati. Symmetries and noncollision closed orbits for planar N-body type problems. Non-linear Anal TMA, 1991, 16: 587-598
5. V Coti Zelati. The periodic solutions of N-body type problems. Ann IHP Anal non linéaire, 1990, 7: 477-492
6. V Coti Zelati. A class of periodic solutions for the AT-body problem. Celestial Mech, 1989, 46: 177-186
7. M Degiovanni, F Giannoni. Dynamical systems with Newtonian type potentials. Ann Scuola Norm Super Pisa, 1989, 15: 467-494
8. E Serra, S Terracini. Collisionless periodic solutions to some three-body problems. Arch Rational Mech Anal, 1992, 120: 305-325
9. C Siegle, J Moser. Lectures on Celestial Mechanics. Berlin: Springer, 1971
10. W Gordon. A minimizing property of Keplerian orbits. Amer J Math, 1977, 99: 961-971
11. G Hardy, J Littlewood, G Polya. Inequalities. 2nd ed, Cambridge: University Press, 1952
12. V Arnold, V Kozlov, A Neishtadt. Dynamical Systems, III, Mathematical Aspectc of Classical and Celestial Mechanics. Russian ed 1985, Berlin: Spinger, English ed, 1988
13. K Meyer, G Hall. Introduction to Hamiltonian Systems and the N-body problems. Berlin: Springer, 1992
14. A Wintner. Analytical Foundations of Celestial Mechanics. Princeton: Princeton University Press, 1941
15. J Lagrange. Essai sur le probléme des trois corps. 1772, Ouvres, 1783, 3: 229-331
16. R Abraham, J Marsden. Foundations of Mechanics. 2nd ed, London: Benjamin/Cummings, 1978
17. L Euler. De motu rectilineo trium corpörum se mutuo attrahentium. Novi Comm Acad Sci Imp Petropll, 1767, 145-151.
18. J H Wang. The Three Body Problem. Chinese ed, Beijing: Science Press, 1961