90 Result(s)
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Alessandra Celletti
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Article
From infinite to finite time stability in Celestial Mechanics and Astrodynamics
Time scales in Celestial Mechanics and Astrodynamics vary considerably, from a few hours for the motion of Earth’s artificial satellites to millions of years for planetary dynamics. Hence, the time scales on w...
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Article
Open AccessAccurate Computations up to Breakdown of Quasi-Periodic Attractors in the Dissipative Spin–Orbit Problem
We consider a Celestial Mechanics model: the spin–orbit problem with a dissipative tidal torque, which is a singular perturbation of a conservative system. The goal of this paper is to show that it is possible...
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Article
Open AccessOld perturbative methods for a new problem in Celestial Mechanics: the space debris dynamics
Perturbative methods have been developed and widely used in the XVIII and XIX century to study the behavior of N-body problems in Celestial Mechanics. Such methods apply to nearly-integrable Hamiltonian systems a...
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Article
Open AccessNekhoroshev estimates for the orbital stability of Earth’s satellites
We provide stability estimates, obtained by implementing the Nekhoroshev theorem, in reference to the orbital motion of a small body (satellite or space debris) around the Earth. We consider a Hamiltonian mode...
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Living Reference Work Entry In depth
Perturbation Theory in Celestial Mechanics
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Article
Open AccessThe Spin–Spin Problem in Celestial Mechanics
We study the dynamics of two homogeneous rigid ellipsoids subject to their mutual gravitational influence. We assume that the spin axis of each ellipsoid coincides with its shortest physical axis and is perpen...
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Article
The Role of Tidal Forces in the Long-term Evolution of the Galilean System
The Galilean satellites of Jupiter are called Io, Europa, Ganymede and Callisto. The first three moons are found in the so-called Laplace resonance, which means that their orbits are locked in a
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Article
Open AccessProper elements for space debris
Proper elements are quasi-invariants of a Hamiltonian system, obtained through a normalization procedure. Proper elements have been successfully used to identify families of asteroids, sharing the same dynamical ...
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Article
Open AccessClassification of regular and chaotic motions in Hamiltonian systems with deep learning
This paper demonstrates the capabilities of convolutional neural networks (CNNs) at classifying types of motion starting from time series, without any prior knowledge of the underlying dynamics. The paper appl...
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Reference Work Entry In depth
Perturbation Theory in Celestial Mechanics
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Chapter and Conference Paper
KAM Theory for Some Dissipative Systems
Dissipative systems play a very important role in several physical models, most notably in Celestial Mechanics, where the dissipation drives the motion of natural and artificial satellites, leading them to mig...
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Chapter and Conference Paper
Resonant Dynamics of Space Debris
Since the launch of the Sputink 1 in 1957, a number of debris accumulated and now populates the circumterrestrial environment. These objects are found from Low Earth Orbits at altitudes of a few hundreds of ki...
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Article
Efficient and Accurate KAM Tori Construction for the Dissipative Spin–Orbit Problem Using a Map Reduction
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. Our goal is to ...
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Article
Open AccessReconnecting groups of space debris to their parent body through proper elements
Satellite collisions or fragmentations generate a huge number of space debris; over time, the fragments might get dispersed, making it difficult to associate them to the configuration at break-up. In this work...
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Article
Open AccessSemi-Analytical Estimates for the Orbital Stability of Earth’s Satellites
Normal form stability estimates are a basic tool of Celestial Mechanics for characterizing the long-term stability of the orbits of natural and artificial bodies. Using high-order normal form constructions, we...
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Article
Hill Four-Body Problem with Oblate Bodies: An Application to the Sun–Jupiter–Hektor–Skamandrios System
We consider a restricted four-body problem, with a precise hierarchy between the bodies: two larger bodies and a smaller one, all three of oblate shape, and a fourth, infinitesimal body, in the neighborhood of...
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Article
Topical collection “50 years of Celestial Mechanics and Dynamical Astronomy”
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Article
The dynamics of the de Sitter resonance
We study the dynamics of the de Sitter resonance, namely the stable equilibrium configuration of the first three Galilean satellites. We clarify the relation between this family of configurations and the more ...
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Article
Editorial
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Article
Geostationary secular dynamics revisited: application to high area-to-mass ratio objects
The long-term dynamics of the geostationary Earth orbits (GEO) is revisited through the application of canonical perturbation theory. We consider a Hamiltonian model accounting for all major perturbations: geo...
