Bifurcation points and intersections of families of periodic orbits in the three-dimensional restricted three-body problem

Details Bifurcation points and intersections of families of periodic orbits in the three-dimensional restricted three-body problem Bifurcation points and intersections of families of periodic orbits in the three-dimensional restricted three-body problem

Jan 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993ap%26ss.199..241p&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 199, no. 2, p. 241-256.

Mathematics

3

Branching (Mathematics), Orbital Mechanics, Three Body Problem, Three Dimensional Models, Equations Of Motion, Lagrangian Equilibrium Points

Scientific paper

Intersections of families of 3D periodic orbits which define bifurcation points are studied. The existence conditions for bifurcation points are discussed and an algorithm for the numerical continuation of such points is developed. Two sequences of bifurcation points are given concerning the family of periodic orbits which starts and terminates at the triangular equilibrium points L4, L5. On these sequences two trifurcation points are identified for mu = 0.124214 and mu = 0.399335. The case mu = 0.5 is studied in particular and it is found that the space families originating at the equilibrium points L2, L3, L4, L5 terminate on the same planar orbit m(lv) of the family m.

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