Bifurcations of plane with three-dimensional periodic orbits in the elliptic restricted problem

Details Bifurcations of plane with three-dimensional periodic orbits in the elliptic restricted problem Bifurcations of plane with three-dimensional periodic orbits in the elliptic restricted problem

Jan 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981cemec..23...97r&link_type=abstract

Celestial Mechanics, vol. 23, Jan. 1981, p. 97-106.

Mathematics

2

Elliptical Orbits, Orbital Mechanics, Periodic Variations, Three Dimensional Motion, Branching (Mathematics), Motion Stability, Orbital Resonances (Celestial Mechanics), Series Expansion, Trajectory Analysis

Scientific paper

It is shown that the procedure employed in the circular restricted problem, of tracing families of three-dimensional periodic orbits from vertical self-resonant orbits belonging to plane families, can also be applied in the elliptic problem. A method of determining series of vertical bifurcation orbits in the planar elliptic restricted problem is described, and one such series consisting of vertical-critical orbits is given for the entire range of the mass parameter mu. The initial segments of the families of three-dimensional orbits which bifurcate from two of the orbits belonging to this series are also given.

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