The inclination changes in the problem of two triaxial rigid spheroids

The first-order perturbations of a system of two triaxial rigid spheroids under Hori-Lie transformation are investigated. The time dependence of the configuration of the three angular momentum vectors, two rotational and one orbital, is studied. The problem is simplified by the introduction of a new time parameter , such thatt is the hyperelliptic function of . The projectionsH ₁ andH ₂ of the rotational momentum vectors into the direction of the total angular momentum vector of the system are then harmonic or exponential functions of . The trajectory in theH ₁,H ₂ plane is a part of an ellipse or hyperbola respectively. If this conical section intersects a certain critical contourC, the system is bounced back along the original trajectory. The motion of the relative configuration of the angular momentum vectors is periodical except in a special aperiodic case. The expressions for the periods are given.