Triple collisions in the one-dimensional three-body problem

Celestial Mechanics and Dynamical Astronomy

Volumn 76, Issue 1, 2000, Pages 23-34

  Tanikawa, Kiyotaka ^a   Mikkola, Seppo ^b  

^a NATIONAL ASTRONOMICAL OBSERVATORY OF JAPAN   (Japan)

^b UNIVERSITY OF TURKU   (Finland)

Author keywords

Chaos; One dimensional three body problem; Triple collision

Indexed keywords

EID: 0002028292     PISSN: 09232958     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008397420958     Document Type: Article

References (10)

1. Bulirsch, R. and Stoer, J.: 1966, 'Numerical treatment of differential equations by extrapolation methods', Num. Math. 8, 1-13.
2. McGehee, R.: 1974, 'Triple collision in the collinear three-body problem', Inventiones Mathematicae 27, 191-227.
3. Mikkola, S. and Hietarinta, J.: 1989, 'A numerical investigation of the one-dimensional Newtonian three-body problem', Celest. Mech. & Dyn. Astr. 46, 1-18.
4. Mikkola, S. and Hietarinta, J.: 1990, 'A numerical investigation of the one-dimensional Newtonian three-body problem. II positive energies', Celest. Mech. & Dyn. Astr. 47, 321-331.
5. Mikkola, S. and Hietarinta, J.: 1991, 'A numerical investigation of the one-dimensional Newtonian three-body problem. III. mass dependence in the stability of motion', Celest. Mech. & Dyn. Astr. 51, 379-394.
6. Hietarinta, J. and Mikkola, S.: 1993, Chaos in the one-dimensional Newtonian three-body problem', Chaos 3(2), 183-203.
7. Tanikawa, K., Umehara, H. and Abe, H.: 1995, 'A search for collision orbits in the free-fall three-body problem I. Numerical procedure', Celest. Mech. & Dyn. Astr. 62, 335-362.
8. Tanikawa, K. and Umehara, H.: 1998, 'Oscillatory orbits in the planar three-body problem with equal masses', Celest. Mech. & Dyn. Astr. 70, 167-180.
9. Yoshida, H.: 1987, 'A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential', Physica 29D, 128-142.
10. Yoshida, H.: 1988, Non-integrability of the three-body problems with homogeneous potential. In: M. J. Valtonen (ed.), The Few-Body Problem, Proceedings of the 96th colloquium of the IAU, Turku, Finland 1987, Kluwer Academic Publishers, 1988.