47 citations · 762 across the 57 of their papers we have counts for
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Dynamical Stability of the Laplace Resonance
Giuseppe Pucacco
We analyse the stability of the de Sitter equilibria in multi-resonant planetary systems. The de Sitter equilibrium is the dynamical state of the Laplace resonance in which all res…
Proper Elements for Space Debris
Alessandra Celletti, Giuseppe Pucacco, Tudor Vartolomei
Proper elements are quasi-invariants of a Hamiltonian system, obtained through a normalization procedure. Proper elements have been successfully used to identify families of astero…
Laplace-like resonances with tidal effects
A. Celletti, E. Karampotsiou, C. Lhotka +2
We generalize the Laplace resonance among three satellites, S1, S2 , and S3, by considering different ratios of the mean-longitude variations. These resonances, which we call Lapla…
Normal forms for the Laplace resonance
Giuseppe Pucacco
We describe a comprehensive model for systems locked in the Laplace resonance. The framework is based on the simplest possible dynamical structure provided by the Keplerian problem…
Accurate modelling of the low-order secondary resonances in the spin-orbit problem
Ioannis Gkolias, Christos Efthymiopoulos, Alessandra Celletti +1
We provide an analytical approximation to the dynamics in each of the three most important low order secondary resonances (1:1, 2:1, and 3:1) bifurcating from the synchronous prima…
Element history of the Laplace resonance: a dynamical approach
Fabrizio Paita, Alessandra Celletti, Giuseppe Pucacco
We consider the three-body mean motion resonance defined by the Jovian moons Io, Europa, and Ganymede, which is commonly known as the Laplace resonance. In particular, we construct…
The dynamics of the de Sitter resonance
Alessandra Celletti, Fabrizio Paita, Giuseppe Pucacco
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…
Hamiltonian formulation of the spin-orbit model with time-varying non-conservative forces
Ioannis Gkolias, Christos Efthymiopoulos, Giuseppe Pucacco +1
In a realistic scenario, the evolution of the rotational dynamics of a celestial or artificial body is subject to dissipative effects. Time-varying non-conservative forces can be d…
Dynamical models and the onset of chaos in space debris
Alessandra Celletti, Christos Efthymiopoulos, Fabien Gachet +2
The increasing threat raised by space debris led to the development of different mathematical models and approaches to investigate the dynamics of small particles orbiting around t…
Geostationary secular dynamics revisited: application to high area-to-mass ratio objects
Fabien Gachet, Alessandra Celletti, Giuseppe Pucacco +1
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…
The theory of secondary resonances in the spin-orbit problem
Ioannis Gkolias, Alessandra Celletti, Christos Efthymiopoulos +1
We study the resonant dynamics in a simple one degree of freedom, time dependent Hamiltonian model describing spin-orbit interactions. The equations of motion admit periodic soluti…
Bifurcations of lunisolar secular resonances for space debris orbits
Alessandra Celletti, Cătălin Galeş, Giuseppe Pucacco
Using bifurcation theory, we study the secular resonances induced by the Sun and Moon on space debris orbits around the Earth. In particular, we concentrate on a special class of s…
Analytical development of the lunisolar disturbing function and the critical inclination secular resonance
Alessandra Celletti, Cătălin Galeş, Giuseppe Pucacco +1
We provide a detailed derivation of the analytical expansion of the lunar and solar disturbing functions. Although there exist several papers on this topic, many derivations contai…
Normal forms for the epicyclic approximations of the perturbed Kepler problem
Giuseppe Pucacco
We compute the normal forms for the Hamiltonian leading to the epicyclic approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian setting corresponds to the d…