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Stability and Chaos in Celestial Mechanics
No full textThis book presents classical celestial mechanics and its interplay with dynamical systems in a way suitable for advance level undergraduate students as well as postgraduate students and researchers. First paradigmatic models are used to introduce the reader to the concepts of order, chaos, invariant curves, cantori. Next the main numerical methods to investigate a dynamical system are presented. Then the author reviews the classical two-body problem and proceeds to explore the three-body model in order to investigate orbital resonances and Lagrange solutions. In rotational dynamics the author details the derivation of the rigid body motion, and continues by discussing related topics, from spin-orbit resonances to dumbbell satellite dynamics.
Perturbation theory is then explored in full detail including practical examples of its application to finding periodic orbits, computation of the libration in longitude of the Moon. The main ideas of KAM theory are provided including a presentation of long-term stability and converse KAM results. Celletti then explains the implementation of computer-assisted techniques, which allow the user to obtain rigorous results in good agreement with the astronomical expectations. Finally the study of collisions in the solar system is approached
The laplace resonance: between theory and space missions
No full textThe Galilean satellites of Jupiter - Io, Europa, and Ganymede - are observed to move in a dynamical configuration known as the "Laplace resonance". It means that the pairs of satellites Io-Europa and Europa-Ganymede are characterized by a 2:1 ratio between their mean longitudes through a relation involving also the arguments of perijoves. Another dynamical configuration is known as the "de Sitter resonance" in which a certain combination of mean longitudes and arguments of perijoves librates, while it rotates in the Laplace resonance. In view of the space mission JUICE, which will be launched in 2022 towards Jupiter and three of its largest moons, we investigate the dynamics of both resonances using a suitable normal form that allows to describe the resonant Laplace and de Sitter configurations. We review a series of papers in collaboration with F. Paita and G. Pucacco ([8], [30], [9]), where we study the evolution of the Laplace librating argument and, among other results, we provide an estimate on its amplitude and frequency
Analysis of resonances in the spin-orbit problem in Celestial Mechanics: the synchronous resonance (Part I)
No full textRigorous and numerical determination of rotational invariant curves for the standard map
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Analysis of resonances in the spin-orbit problem in Celestial Mechanics: Higher order resonances and some numerical experiments (Part II)
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