86,689 research outputs found
Invariant curves for area-preserving twist maps far from integrable
No full textOne-parameter families of area-preserving twist maps of the form F-epsilon(x, y) = (x + y + epsilon-f(x), y + epsilon-f(x)) are considered. Various invariant curves, for the maps corresponding to f(x) = sin x and f(x) = sin x + (1/50) sin(5x), are rigorously constructed for large values of the nonlinearity parameter-epsilon. For larger values of epsilon, close to critical, some numerical experiments are briefly discussed
Corrigendum: Plasticity Induced in the Human Spinal Cord by Focal Muscle Vibration
No full textCorrigendum: Plasticity Induced in the Human Spinal Cord by Focal Muscle Vibration by Rocchi, L., Suppa, A., Leodori, G., Celletti, C., Camerota, F., Rothwell, J., et al. (2018). Front. Neurol. 9:935. doi: 10.3389/fneur.2018.00935
The dynamics of the de Sitter resonance
No full textWe 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 general Laplace resonant states. In order to describe the dynamics around the de Sitter stable equilibrium, a one-degree of freedom Hamiltonian normal form is constructed and exploited to identify initial conditions leading to the two families.
The normal form Hamiltonian is used to check the accuracy in the location of the equilibrium positions. Besides, it gives a measure of how sensitive it is with respect to the different perturbations acting on the system. By looking at the phase-plane of the normal form, we can identify a \sl Laplace-like \rm configuration, which highlights many substantial aspects of the observed one
Element history of the Laplace resonance: A dynamical approach
No full textContext. 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 terms of the moons' mean longitudes lambda(1) (Io), lambda(2) (Europa), and lambda(3) (Ganymede), this resonance is described by the librating argument phi(L) lambda(1) - 3 lambda(2) + 2 lambda(3)( )approximate to 180 degrees, which is the sum of phi(12) lambda(1) - 2 lambda(2) + pi(2) approximate to 180 degrees and phi(23) lambda(2) - 2 lambda(3) pi(2)( )approximate to 0 degrees, where pi(2) denotes Europa's longitude of perijove.Aims. In particular, we construct approximate models for the evolution of the librating argument phi(L) over the period of 100 yr, focusing on its principal amplitude and frequency, and on the observed mean motion combinations n(1) - 2n(2) and n(2) - 2n(3) associated with the quasi-resonant interactions above.Methods. First, we numerically propagated the Cartesian equations of motion of the Jovian system for the period under examination, and by comparing the results with a suitable set of ephemerides, we derived the main dynamical effects on the target quantities. Using these effects, we built an alternative Hamiltonian formulation and used the normal forms theory to precisely locate the resonance and to semi-analytically compute its main amplitude and frequency.Results. From the Cartesian model we observe that on the timescale considered and with ephemerides as initial conditions, both phi(L) and the diagnostics n(1) - 2n(2) and n(2) - 2n(3) are well approximated by considering the mutual gravitational interactions of Jupiter and the Galilean moons (including Callisto), and the effect of Jupiter's J(2) harmonic. Under the same initial conditions, the Hamiltonian formulation in which Callisto and J(2) are reduced to their secular contributions achieves larger errors for the quantities above, particularly for phi(L) . By introducing appropriate resonant variables, we show that these errors can be reduced by moving in a certain action-angle phase plane, which in turn implies the necessity of a tradeoff in the selection of the initial conditions.Conclusions. In addition to being a good starting point for a deeper understanding of the Laplace resonance, the models and methods described are easily generalizable to different types of multi-body mean motion resonances. Thus, they are also prime tools for studying the dynamics of extrasolar systems
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
Geostationary secular dynamics revisited: application to high area-to-mass ratio objects
No full textThe 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: geopotential at order and degree two, lunisolar per- turbations with a realistic model for the Sun and Moon orbits, and solar radiation pressure. The long-term dynamics of the GEO region has been studied both numerically and analyti- cally, in view of the relevance of such studies to the issue of space debris or to the disposal of GEO satellites. Past studies focused on the orbital evolution of objects around a nom- inal solution, hereafter called the forced equilibrium solution, which shows a particularly strong dependence on the area-to-mass ratio. Here, we (i) give theoretical estimates for the long-term behavior of such orbits, and (ii) we examine the nature of the forced equilibrium itself. In the lowest approximation, the forced equilibrium implies motion with a constant non-zero average ‘forced eccentricity’, as well as a constant non-zero average inclination, otherwise known in satellite dynamics as the inclination of the invariant ‘Laplace plane’. Using a higher order normal form, we demonstrate that this equilibrium actually represents not a point in phase space, but a trajectory taking place on a lower-dimensional torus. We give analytical expressions for this special trajectory, and we compare our results to those found by numerical orbit propagation. We finally discuss the use of proper elements, i.e., approximate integrals of motion for the GEO orbits
The dynamics of Laplace-like resonances
No full textThe three inner Galilean satellites of Jupiter-Io, Europa, and Ganymede-are observed to move in a particular dynamical configuration, which is commonly known as the Laplace resonance. These satellites are characterized by a 2:1 ratio between the mean longitudes of Io-Europa and Europa-Ganymede. Another dynamical configuration, known as the de Sitter resonance, occurs when the longitude of Ganymede is fixed, instead of rotating like in the Laplace resonance. Besides studying the Laplace and de Sitter resonances, we also consider their generalizations to the case in which the mean longitudes of the first two satellites are in a ratio k:j, while those of the second and third satellites are in a ratio m:n with k,j,m,n∈Z+ and |j-k|, |n-m|≤2. We derive a model apt to describe such resonant configurations. We make an extensive study of the structural stability of the resonances; we show that the libration of the Laplace resonant angle is deeply affected by small variations of some quantities, most notably the semimajor axes and the oblateness. A remarkable result is that in several cases, the standard Laplace resonance of the Galilean satellites displays a regular behavior in comparison to other resonances characterized by different mean longitude ratios, which instead show a rather chaotic behavior even on short time scales. This result provides a motivation to support why the Galilean satellites are found in the actual Laplace resonance
Dynamical models and the onset of chaos in space debris
No full textThe 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 the Earth. The choice of such models and methods strongly depend on the altitude of the objects above Earth's surface, since the strength of the different forces acting on an Earth orbiting object (geopotential, atmospheric drag, lunar and solar attractions, solar radiation pressure, etc.) varies with the altitude of the debris.
In this review, our focus is on presenting different analytical and numerical approaches employed in modern studies of the space debris problem. We start by considering a model including the geopotential, solar and lunar gravitational forces and the solar radiation pressure. We summarize the equations of motion using different formalisms: Cartesian coordinates, Hamiltonian formulation using Delaunay and epicyclic variables, Milankovitch elements. Some of these methods lead in a straightforward way to the analysis of resonant motions. In particular, we review results found recently about the dynamics near tesseral, secular and semi-secular resonances.
As an application of the above methods, we proceed to analyze a timely subject, namely the possible causes for the onset of chaos in space debris dynamics. Precisely, we discuss the phenomenon of overlapping of resonances, the effect of a large area-to-mass ratio, the influence of lunisolar secular resonances.
We conclude with a short discussion about the effect of the dissipation due to the atmospheric drag and we provide a list of minor effects, which could influence the dynamics of space debris
PROCEDIMENTO DI STAMPA
No full textL'invenzione concerne un innovativo procedimento di stampa su
supporti realizzati principalmente in gomma di pneumatico da riciclo. Il procedimento consente di decorare mediante
stampa ad inchiostro manufatti in gomma, da riciclo di pneumatico, realizzati senza aggiunta di alcun legante o materiale vergine. Il procedimento prevede l’utilizzo di polverino di gomma con o senza granuli
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