Crash test for the Copenhagen problem

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 69, Issue 6 2, 2004, Pages

  Nagler, Jan ^a  

^a UNIVERSITY OF BREMEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CHAOS THEORY; COMPUTATION THEORY; ELECTRON ENERGY LEVELS; EQUATIONS OF MOTION; GRAVITATION; HAMILTONIANS; LAGRANGE MULTIPLIERS; ORBITS; SOLAR SYSTEM;

CHAOTIC SCATTERING THEORY; COPHENHAGEN PROBLEM; KEPLER FREQUENCY; ORBIT TYPE DIAGRAMS (OTD);

ASTROPHYSICS;

EID: 42749103712     PISSN: 15393755     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.69.066218     Document Type: Article

References (27)

1. V. Szebehely, Theory of Orbits (Academic Press, New York, 1967).
2. M. Hénon, Bull. Astron. 1, 57 (1966).
3. M. Hénon, Bull. Astron. 1, 49 (1966).
4. M. Hénon, Generating Families in the Restricted Three-Body Problem (Springer-Verlag, Berlin, 1997).
5. M. Hénon, Generating Families in the Restricted Three-Body Problem. II. Quantitative Study of Bifurcations (Springer-Verlag, Berlin, 2001).
6. P. H. Richter, Rev. Mod. Astron. 14, 53 (2001).
7. A. F. Brunello, T. Uzer, and D. Farrelly, Phys. Rev. A 55, 3730 (1997).
8. E. Lee, A. F. Brunello, and D. Farrelly, Phys. Rev. A 55, 2203 (1997).
9. M. A. Murison, Astron. J. 98, 2346, 2383 (1989).
10. T. I. Maindl and R. Dvorak, Astron. Astrophys. 290, 335 (1994).
11. N. Haghighipour, Mon. Not. R. Astron. Soc. 304, 185 (1998).
12. N. Haghighipour, Mon. Not. R. Astron. Soc. 316, 845 (1999).
13. J. Liebert and W. B. Hubbard, Nature (London) 400, 316 (1999).
14. J. J. Lissauer, Nature (London) 419, 355 (2002).
15. S. A. Astakhov, A. D. Burbanks, S. Wiggins, and D. Farrelly, Nature (London) 423, 264 (2003).
16. G. D. Quinlan, New Astron. 1, 35 (1996).
17. H. Poincaré, Les Méthodes Nouvelles de la Mécanique Céleste (Gauthier-Villars, Paris, 1892), translated by the AIP, History of Modern Physics and Astronomy, 1993, Vol. 13.
18. H. Poincaré, Les Méthodes Nouvelles de la Mécanique Céleste (Gauthier-Villars, Paris, 1892), translated by the AIP, History of Modern Physics and Astronomy, 1993, Vol. 13.
19. H. R. Dullin and A. Wirtek, J. Phys. A 28, 7157 (1995).
20. J. Nagler, Ph.D. thesis, Universität Bremen 2002.
21. Y. Hagihara, Celestial Mechanics. Vol. IV. Part 1, 2: Periodic and Quasi-Periodic Solutions (Japan Society for the Promotion of Science, Tokyo, 1975, Vol. XV, p. 1243).
22. S. Bleher, C. Grebogi, E. Ott, and R. Brown, Phys. Rev. A 38, 930 (1988).
23. A. P. S. de Moura and C. Grebogi, Phys. Rev. E 66, 046214 (2002).
24. J. Schneider, T. Tél, and Z. Neufeld, Phys. Rev. E 66, 066218 (2003).
25. J. Nagler, "Bifurcation schemes in the restricted three-body problem," in preparation.
26. The distance between the two primaries is scaled to unity and a time unit is related to the unit angular velocity of the primaries, i.e., one rotation corresponds to 2π time units.
27. in=E+L.