Physics
Scientific paper
Apr 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979cemec..19..263m&link_type=abstract
Celestial Mechanics, vol. 19, Apr. 1979, p. 263-277.
Physics
11
Euler-Lagrange Equation, Orbital Mechanics, Three Body Problem, Celestial Mechanics
Scientific paper
It is demonstrated that monoparametric families of three-dimensional periodic orbits can be derived from the vertical critical orbits of the general planar formulation of the three-body problem. Vertical critical orbits symmetric with respect to the x-axis can be used to determine three-dimensional periodic orbits of the general problem which are symmetric with respect to the xz-plane or to the x-axis or to both the xz-plane and x-axis of a suitably defined rotating frame of reference. When the mass of the third body is zero, this rotating frame of reference reduces to the usual rotating frame of the restricted problem. Numerical examples of three-dimensional periodic orbit determinations are presented.
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