A numerical investigation of the one-dimensional Newtonian three-body problem. III - Mass dependence in the stability of motion

Details A numerical investigation of the one-dimensional Newtonian three-body problem. III - Mass dependence in the stability of motion A numerical investigation of the one-dimensional Newtonian three-body problem. III - Mass dependence in the stability of motion

Dec 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991cemda..51..379m&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 51, no. 4, 1991, p. 379-394.

Astronomy and Astrophysics

Astronomy

14

Motion Stability, Newton Methods, Orbital Mechanics, Three Body Problem, Eigenvalues, Mass Distribution, Nonlinear Systems, Three Dimensional Models

Scientific paper

The 1D Newtonian three-body problem is known to have stable (quasi-)periodic orbits when the masses are equal. The existence and size of the stable region is discussed here in the case where the three masses are arbitrary. Only the stability of the periodic (generalized) Schubart's (1956) orbit is considered. If this orbit is linearly stable, it is almost always surrounded by a region of stable quasi-periodic orbits and the size and shape of this stable region depends on the masses. The 3D linear stability of the periodic orbits is also determined. Final results show that the region of stability has a complicated shape and some of the stable regions in the mass-plane are quite narrow. The nonlinear 3D stability is studied independently by extensive numerical integrations, and the results are found to be in agreement with the linear stability analysis. The boundaries of stable region in the mass-plane are given in terms of polynomial approximations.

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