Transient times, resonances and drifts of attractors in dissipative rotational dynamics

Abstract

In a dissipative system the time to reach an attractor is often influenced by the peculiarities of the model and in particular by the strength of the dissipation. In particular, as a dissipative model we consider the spin-orbit problem providing the dynamics of a triaxial satellite orbiting around a central planet and affected by tidal torques. The model is ruled by the oblateness parameter of the satellite, the orbital eccentricity, the dissipative parameter and the drift term. We devise a method which provides a reliable indication on the transient time which is needed to reach an attractor in the spin-orbit model; the method is based on an analytical result, precisely a suitable normal form construction. This method provides also information about the frequency of motion. A variant of such normal form used to parametrize invariant attractors provides a specific formula for the drift parameter, which in turn yields a constraint - which might be of interest in astronomical problems - between the oblateness of the satellite and its orbital eccentricity.

21 pages, 7 figures, color

References in corpus (1)

• Mercury's capture into the 3/2 spin-orbit resonance including the effect of core-mantle friction

Cited by in corpus (5)

• Excitation of Tumbling in Phobos and Deimos
• Efficient and accurate KAM tori construction for the dissipative spin-orbit problem using a map reduction
• Accurate modelling of the low-order secondary resonances in the spin-orbit problem
• Effective resonant stability of Mercury
• The dynamics of the spin-spin problem in Celestial Mechanics