To the problem of nonlinear oscillations near triangular libration points

A spatial restricted problem of three bodies attracted by Newton's law is studied. The orbits of the main attracting bodies are assumed to be ellipses of small eccentricity. An approximate mathematical model describing nonlinear oscillations of a passively gravitating body near a Lagrangian triangular libration point is obtained using the normal form method. A detailed study of these oscillations is given in a particular case of third-order resonance.This research was carried out within the framework of the state assignment (registration No. 124012500443-0) at the Ishlinsky Institute for Problems in Mechanics RAS.