Mathematics
Scientific paper
Jul 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977mnras.180..103m&link_type=abstract
Monthly Notices of the Royal Astronomical Society, vol. 180, July 1977, p. 103-116. Research supported by the Science Research
Mathematics
16
Branching (Mathematics), Motion Stability, Orbital Mechanics, Periodic Functions, Three Body Problem, Three Dimensional Motion, Astrodynamics, Asymmetry, Equations Of Motion, Orbital Elements, Planetary Orbits, Trajectory Analysis
Scientific paper
The aim of this paper is the detection of three-dimensional asymmetric periodic orbits. An iterative procedure is described for determining the bifurcations of families of plane asymmetric periodic solutions to the restricted three-body problem with such three-dimensional orbits. It is applied to the two previously established bifurcations of this type. For each of them a 'bifurcation series' is obtained, covering the entire range of the mass parameter of the problem. The stability of these bifurcation orbits is examined, and it is found that in each case there are two subintervals of the range of the mass parameter for which these orbits are stable, one of them containing cases of astronomical interest. Typical three-dimensional asymmetric periodic orbits of the bifurcating families are also given.
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