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Celletti Alessandra - Stability and chaos in celestial mechanics


Author : Celletti Alessandra
Title : Stability and chaos in celestial mechanics
Year : 2010

Link download : Celletti_Alessandra_-_Stability_and_chaos_in_celestial_mechanics.zip

Preface. The last decades have marked the beginning of a new era in Celestial Mechanics. The challenges came from several different directions. The stability theory of nearly–integrable systems (a class of problems which includes many models of Celestial Mechanics) profited from the breakthrough represented by the Kolmogorov– Arnold–Moser theory, which also provides tools for determining explicitly the parameter values allowing for stability. A confinement of the actions for exponential times was guaranteed by Nekhoroshev’s theorem, which gives much information about the geography of the resonances. Performing ever-faster computer simulations allowed us to have deeper insights into many questions of Dynamical Systems, most notably chaos theory. In this context several techniques have been developed to distinguish between ordered and chaotic behaviors. Modern tools for computing spacecraft trajectories made possible the realization of many space missions, especially the interplanetary tours, which gave a new shape to the solar system with a lot of new satellites and small bodies. Finally, the improvement of observational techniques allowed us to make two revolutions in the sky : the solar system does not end with Pluto, but it extends to the Kuiper belt, and the solar system is not unique, but the universe has plenty of extrasolar planetary systems. Cooking all these ingredients together with the classical theories developed from the 17th to the 19th centuries, one obtains the modern Celestial Mechanics. In this context the main goal of the CELMEC meetings, conferences which are held every four years on Celestial Mechanics (which I have had the opportunity to co–organize since 1993), is to bring together the analytical aspects (from perturbation theory to stability analysis), the dynamics of the solar system and of stellar interactions, flight dynamics for near–Earth and interplanetary missions. ...

867 lectures

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