Axisymmetric periodic orbits of the restricted problem in three dimensions.
Abstract
A complete family of axisymmetric threedimensional periodic orbits is determined numerically for two cases of the restricted problem (mu equal to 0.00095 and 0.5). This family is found to connect in a continuous evolution Stromgren's families l and m of plane symmetric retrograde periodic orbits around both primaries. The numerical techniques used to trace families of axisymmetric orbits and to determine their stability by integrating for only half the period are outlined. From the symplectic property of the variational matrix of the solutions to the restricted problem, special linear relations connecting various elements of this matrix are derived.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 July 1977
 Bibcode:
 1977A&A....59...79Z
 Keywords:

 Celestial Mechanics;
 Orbit Calculation;
 Orbits;
 Three Body Problem;
 Equations Of Motion;
 Periodic Variations;
 Astronomy