On Resonant Values of Parameters in the Problem on the Stability of Lagrangian Solutions in the Near-Circular Restricted Three-Body Problem

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Abstract
The restricted problem of three bodies (material points) moving under the action of gravitational attraction according to Newton’s law is considered. The orbits of the main attracting bodies are considered to be ellipses with a small eccentricity, and a passively gravitating body can perform arbitrary spatial motion near the triangular libration point. For the Hamiltonian function corresponding to such a motion, the structure of the normal form is pointed in the cases of third-order resonances. In the planar restricted three-body problem, the equations up to the second degree of eccentricity for resonance curves for all resonances up to the sixth order inclusive are obtained.