Mathematics
Scientific paper
Sep 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981cemec..25....3m&link_type=abstract
Celestial Mechanics, vol. 25, Sept. 1981, p. 3-31. Research supported by the Science Research Council.
Mathematics
11
Branching (Mathematics), Celestial Mechanics, Orbit Calculation, Three Body Problem, Dynamic Stability, Equations Of Motion, Matrices (Mathematics), Partial Differential Equations, Variational Principles
Scientific paper
The generation of three-dimensional periodic orbits of the general three-body problem from special generating plane orbits, the vertical-critical orbits, is studied. The bifurcation process is examined analytically and geometrically. A method of obtaining numerically continuous sets of vertical-critical orbits is outlined, and applied for the determination of 16 monoparametric sets including all possible types of such orbits corresponding to all possible types of symmetry of the bifurcating three-dimensional orbits. The stability of all bifurcation orbits is assessed. Examples of three-dimensional periodic orbits generated from the bifurcation orbits are given.
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