Normal forms and KAM theory in Celestial Mechanics: from space debris to the rotation of the Moon

Since centuries, Celestial Mechanics is a test-bench for many theories of Dynamical Systems, among which perturbation theory and KAM theory. Realistic results in astronomical applications can be obtained through an accurate modeling and an appropriate study of the dynamics, which often requires a heavy computational effort.

After an overview on normal forms and (conservative and dissipative) KAM theory, I will consider some examples in Celestial Mechanics, where such theories give successful results.
In particular, I will review some results about the dynamics of space debris, which can be studied through averaging theory and normal forms computations. The stability of the rotation of the Moon, as well as the
orbital motion of asteroids in the framework of a particular 3-body problem, can be investigated through computer-assisted implementations of KAM theory.

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