We focus on the equations of motion related to the "dissipative spin-orbit model", which is commonly studied in Celestial Mechanics. We consider them in the more general framework of a 2n-dimensionalaction-angle phase space. Since the friction terms are assumed to be linear and isotropic with respect to the action variables, the Kolmogorov's normalization algorithm for quasi-integrable Hamiltonians can be easily adapted to the dissipative system considered here. This allows us to prove the existence of quasi-periodic invariant tori that are local attractors
International audienceWe perform an analysis of the dynamics of the circular, restricted, planar three-body problem under the effect of different kinds of dissipation (linear, Stokes and Poynting-Robertson drags). Since the problem is singular, we implement a regularization technique in the style of Levi-Civita. The effect of the dissipation is often to decrease the semi-major axis; as a consequence the minor body collides with one of the primaries. In general, it is quite difficult to find non-collision orbits using random initial conditions. However, by means of the computation of the Fast Lyapunov Indicators (FLI), we obtain a global view of the dynamics. Precisely, we detect the regions of the phase space potentially belonging to basins of attraction. This investigation provides information on the different regions of the phase space, showing both collision and non-collision trajectories. Moreover, we find periodic orbit attractors for the case of linear and Stokes drags, while in the case of the Poynting-Robertson effect no other attractors are found beside the primaries, unless a fourth body is added to counterbalance the dissipative effect
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