The three-dimensional general three-body problem - Determination of periodic orbits

Physics

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Celestial Mechanics, Orbit Calculation, Orbital Mechanics, Three Body Problem, Coordinates, Equations Of Motion, Periodic Variations, Symmetry

Scientific paper

The three-dimensional general three-body problem is formulated suitably for the numerical determination of periodic orbits either directly or by continuation from the three-dimensional periodic orbits of the restricted problem. The symmetry properties of the equations of motion are established and the algorithms for the numerical determination of families of periodic orbits are outlined. A normalization scheme based on the concept of the invariable plane is introduced to simplify the process. All three types of symmetric orbit, as well as the general type of asymmetric orbit, are considered. Many three-dimensional periodic orbits are given.

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