A family of symmetrical schubart-like interplay orbits and their stability in the one-dimensional four-body problem

Celestial Mechanics and Dynamical Astronomy

Volumn 94, Issue 1, 2006, Pages 37-65

  Sweatman, Winston L ^a  

^a MASSEY UNIVERSITY   (New Zealand)

Author keywords

Collinear motion; Four body problem; Interplay motions; Periodic orbits

Indexed keywords

EID: 32944462812     PISSN: 09232958     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10569-005-2289-8     Document Type: Review

References (26)

1. Aarseth, S. J. and Zare, K.: 1974, 'A regularization of the three-body problem', Celest. Mech. Dynam. Astron. 10 185-205.
2. Dvorak, R., Contopoulos, G., Efthymiopoulos, Ch. and Voglis, N.: 1998, '"Stickiness" in mappings and dynamical systems', Planet. Space Sci. 46, 1567-1578.
3. Fehlberg, E.: 1968, NASA TR-R-287.
4. Hénon, M.: 1974, 'Families of periodic orbits in the three-body problem', Celest. Mech. Dynam. Astron. 10, 375-388.
5. Hénon, M.: 1976, 'A Family of periodic orbits of the planar three-body problem, and their stability', Celest. Mech. Dynam. Astron. 13, 267-285.
6. Hénon, M.: 1977, 'Stability of interplay motions', Cel. Mech., 15, 243-261.
7. Hietarinta, J. and Mikkola, S.: 1993, 'Chaos in the one-dimensional gravitational three-body problem', Chaos. 3(2), 183-203.
8. Martynova, A. I., Orlov, V. V. and Rubinov, A. V.: 2003, 'Metastability in the evolution of triple systems', Mon. Not. R. Astron. Soc. 344, 1091-1096.
9. McGehee, R.: 1974, 'Triple collision in the collinear three-body problem', Inv. Math. 27, 191-227.
10. Mikkola, S. and Aarseth, S. J.: 1993, An implementation of N-body chain regularization', Celest. Mech. Dynam. Astron. 57, 439-459.
11. Mikkola, S. and Aarseth, S. J.: 1996, A slow-down treatment of close binaries', Celest. Mech. Dynam. Astron. 64, 197.
12. Mikkola, S. and Hietarinta, J.: 1989, 'A numerical investigation of the one-dimensional Newtonian three-body problem', Celest. Mech. Dynam. Astron. 46, 1-18.
13. Mikkola, S. and Hietarinta, J.: 1990, 'A numerical investigation of the one-dimensional Newtonian three-body problem II', Celest. Mech. Dynam. Astron. 47, 321-331.
14. Mikkola, S. and Hietarinta, J.: 1991, 'A numerical investigation of the one-dimensional Newtonian three-body problem III', Celest. Mech. Dynam. Astron. 51, 379-394.
15. Moulton, F. R.: 1910, The straight line solutions of the problem of N bodies', Ann. Math. 12, 1-17.
16. Roy, A. E. and Steves, B. A.: 1998, 'Some special restricted four-body problems - II. From Caledonia to Copenhagen', Planet. Space Sci. 46, 1475-1486.
17. Roy, A. E. and Steves, B. A.: 2000a, 'Restricted four-body problems', Proc. NATO ASI: Restless Universe, Institute of Physics.
18. Roy, A. E. and Steves, B. A.: 2000b, 'The Caledonian symmetrical double binary four-body problem 1: surfaces of zero-velocity using the energy integral', Celest. Mech. Dynam. Astron. 78, 299-318.
19. Schubart, J.: 1956, 'Numerische Aufscuchung periodischer Lösungen im Dreikörperproblem', Astron. Nachr. 283, 17.
20. Sekiguchi, M. and Tanikawa, K.: 2004, 'On the symmetric collinear four-body problem', Publ. Astron. Soc. Jpn. 56, 235-251.
21. Simo, C. and Lacomba, E. A.: 1982, 'Analysis of some degenerate quadruple collisions', Celest. Mech. Dynam. Astron. 28, 49-62.
22. Simo, C. and Lacomba, E. A.: 1992, 'Regularization of simultaneous binary collisions in the n-body problem', J. Differ. Equations. 98, 241-259.
23. Steves, B. A. and Roy, A. E.: 1998, 'Some special restricted four-body problems - I. Modelling the Caledonian problem', Planet. Space Sci. 46 (11/12), 1465-1474.
24. Sweatman, W. L.: 2002, 'The symmetrical one-dimensional Newtonian four-body problem: a numerical investigation'. Celest. Mech. Dynam. Astron. 82, 179-201.
25. Széll, A., Érdi, B., Sándor, Zs. and Steves, B.: 2004, 'Chaotic and stable behaviour in the Caledonian four-body problem', Mon. Not. R. Astron. Soc. 347, 380-388.
26. Whittaker, E. T.: 1937, 'Analytical Dynamics of Particles and Rigid Bodies', fourth edition, Cambridge University Press.