Abstract

We consider the dissipative spin-orbit problem in Celestial Mechanics, which describes the rotational motion of a triaxial satellite moving on a Keplerian orbit subject to tidal forcing and drift. This problem is an example of a conformally symplectic system, which is characterized by the property to transform the symplectic form into a multiple of itself. We construct and continue quasi-periodic solutions with fixed frequency, satisfying appropriate conditions. The construction is based on a KAM theorem for conformally symplectic systems, which also provides estimates on the breakdown threshold of the invariant attractor. To construct the invariant attractor, we will use high precision numerical simulations to compute some of the required quantities. The algorithms are guaranteed to reach arbitrarily close to the border of existence, given enough computer resources.

This talk refers to joint works with A. Celletti, J. Gimeno and R. de la Llave.

References

[1] R. Calleja, A. Celletti, J. Gimeno, R. de la Llave, KAM quasi-periodic tori for the dissipative spin-orbit problem Commun. Nonlinear Sci. Numer. Simul. 106, (2022), 106099

[2] R.Calleja, A.Celletti, J.Gimeno, R.delaLlave, Efficient and accurate KAM tori construction for the dissipative spin orbit problem using a map reduction , Journal of Nonlinear Science volume 32, Article number: 4 (2022)

[3] R. Calleja, A. Celletti, J. Gimeno, R. de la Llave, Accurate computations up to break-down of quasi-periodic attractors in the dissipative spin-orbit problem, preprint: ArXiv 2210.05796

Mathematical Physics and Dynamical Systems Seminar