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In this paper, we have studied the equations of motion for the problem, which are regularised in the neighbourhood of one of the finite masses and the existence of periodic orbits in a three-dimensional coordinate system when  μ  = 0. Finally, it establishes the canonical set ( l ,  L ,  g ,  G ,  h ,  H ) and forms the basic general perturbation theory for the problem.

Periodic orbits in the restricted problem of three bodies in a three-dimensional coordinate system when the smaller primary is a triaxial rigid body