Astronomy and Astrophysics – Astronomy
Scientific paper
Jun 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cemda..46..119d&link_type=abstract
Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 46, no. 2, 1989, p. 119-128.
Astronomy and Astrophysics
Astronomy
2
Celestial Mechanics, Dirichlet Problem, Many Body Problem, Orbit Perturbation, Three Body Problem, Angular Momentum, Equations Of Motion, Orbital Mechanics, Solar System
Scientific paper
Relations between the rectilinear, collinear, and syzygy solutions of the N-body problem are first pointed out. It is shown that, along a solution, the set of the noncollinear syzygy configuration instants is formed by isolated points. Then, the study is restricted to the planar three-body problem and it is proved that, for Dirichlet-stable solutions, a nonsyzygy solution cannot be as close as possible to a syzygy one. It is also true that, in the case of a syzygy solution, the orbit of one particle crosses the line of the other two and cannot be tangent to this line in the transition point. Finally, it is proved that the set of initial conditions leading to noncollinear syzygy solutions is nonempty and open.
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