A contribution to the three-dimensional Copenhagen problem

Details A contribution to the three-dimensional Copenhagen problem A contribution to the three-dimensional Copenhagen problem

Jun 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979a%26a....76....6m&link_type=abstract

Astronomy and Astrophysics, vol. 76, no. 1, June 1979, p. 6-14.

Mathematics

13

Celestial Mechanics, Orbital Elements, Three Body Problem, Three Dimensional Motion, Vertical Motion, Axes Of Rotation, Classifications, Dynamic Stability, Equations Of Motion, Graphs (Charts), Linear Equations, Symmetry, Tables (Data), Transformations (Mathematics)

Scientific paper

The three-dimensional Copenhagen problem is studied numerically for the case where mu equals 0.5. A classification of the vertical critical orbits that are symmetric with respect to both the x and the y axis is given in order to complete Henon's (1973) classification for the case of symmetry with respect to the x axis alone. Several numerical examples of periodic orbits belonging to each of the specified types are presented, along with three new families of three-dimensional periodic orbits.

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