Axisymmetric periodic orbits of the restricted problem in three dimensions

Details Axisymmetric periodic orbits of the restricted problem in three dimensions Axisymmetric periodic orbits of the restricted problem in three dimensions

Jul 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977a%26a....59...79z&link_type=abstract

Astronomy and Astrophysics, vol. 59, no. 1, July 1977, p. 79-89. Research supported by the Science Research Council.

Astronomy and Astrophysics

Astrophysics

31

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

Scientific paper

A complete family of axisymmetric three-dimensional 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.

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