Astronomy and Astrophysics – Astronomy
Scientific paper
Aug 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978mnras.184..273m&link_type=abstract
Monthly Notices of the Royal Astronomical Society, vol. 184, Aug. 1978, p. 273-281. Research supported by the Science Research
Astronomy and Astrophysics
Astronomy
7
Motion Stability, Orbital Mechanics, Periodic Variations, Three Body Problem, Three Dimensional Motion, Asymmetry, Celestial Mechanics, Graphs (Charts), Iterative Solution, Particle Motion
Scientific paper
Henon (1973) conjectured and verified that the passage from vertical stability to instability marks the bifurcation of the family of plane symmetric periodic orbits with a family of three-dimensional (or space) symmetric periodic orbits in the restricted three-body problem. A generalization of this conjecture to the case of a family of plane asymmetric periodic (PAP) orbits bifurcating with families of space asymmetric periodic (SAP) orbits is established by numerical verification of the proposition that the characteristic of a family of simple (M = 1) PAP orbits bifurcates with the characteristic of a family of simple SAP orbits when the vertical stability index takes the value of unity. Two orbits of a family of PAP orbits are determined which satisfy the 'plane to space' bifurcation condition, and an iterative procedure is used to trace completely two bifurcating families of SAP orbits. Four computer plots of a number of orbits are given for each of the two families of SAP orbits.
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