Conditions for Appearance of Strange Attractors in Rotational Dynamics of Small Planetary Satellites

The conditions for the origination of strange attractors in the rotational dynamics of small planetary satellites when they reach a neighborhood of a synchronous resonance separatrix in the course of tidal evolution of the rotary motion are investigated by means of numerical experiments. It is assumed that a satellite has an arbitrary shape and moves along a fixed orbit in the gravitational field of a pointlike mass; its rotational axis is orthogonal to the orbit plane. By calculating Lyapunov exponents, the regions of the values of problem parameters have been found where a strange attractor exists. The possibility of the appearance strange attractor in the rotational dynamics of real small planetary satellites is considered.