On Oscillations in a Neighborhood of Lagrangian Libration Points in One Resonance Case

This paper addresses the spatial restricted elliptic problem of three bodies (material points) gravitating toward each other under Newton’s law of gravitation. The eccentricity of the orbit of the main attracting bodies is assumed to be small, and nonlinear oscillations of a passively gravitating body near a Lagrangian triangular libration point are studied. It is assumed that in the limiting case of the circular problem the ratio of the frequency of rotation of the main bodies about their common center of mass to the value of one of the frequencies of small linear oscillations of the passive body is exactly equal to three. A detailed analysis is made of two different particular cases of influence of the three-dimensionality of the problem on the characteristics of nonlinear oscillations of the passive body.