Conference abstracts

Session B1 - Computational Dynamics - Semi-plenary talk

July 13, 14:30 ~ 15:20 - Room B1

From normal forms to KAM theory, from space debris to the rotation of the Moon

Alessandra Celletti

University of Rome Tor Vergata, Italy   -   celletti@mat.uniroma2.it

Celestial Mechanics is a test-bench for many theories of Dynamical Systems, most notably perturbation theory and KAM theory. Realistic results in concrete applications can be obtained through an accurate modeling and an appropriate study of the dynamics, which often requires a heavy computational effort. After a general discussion on perturbation theory and KAM theorem, I will consider two examples of implementations of normal forms and KAM theory in Celestial Mechanics. The first one concerns the dynamics of space debris, which can be succesfully studied through averaging theory and normal forms computations. The second example analyzes the rotation of the Moon, whose stability can be investigated through a computer-assisted implementation of KAM theory. Perturbation theory and KAM theory can be used also to investigate dissipative systems. In this context, they can give interesting results on the dynamics of space debris at low altitude and possibly on the evolution of the Moon toward its present synchronous rotation.

Joint work with Renato Calleja (National Autonomous University of Mexico, Mexico), Christos Efthymiopoulos (Academy of Athens, Greece), Fabien Gachet (University of Rome Tor Vergata, Italy), Catalin Gales (Al. I. Cuza University, Romania), Rafael de la Llave (Georgia Institute of Technology, USA) and Giuseppe Pucacco (University of Rome Tor Vergata, Italy).

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