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A perturbation method is presented which can be applied to the description of a wide range of physical problems that deal with dynamics of dipolar coupled spins in solids. The method is based on expansion of the operator exponent in a…
We seek periodic trajectories of a system of multiple mutually repelling electrons on a half-line, with an attractive nucleus sitting at the origin. We adopt a variational viewpoint and study critical points of the associated…
We investigate the resonant rotation of co-orbital bodies in eccentric and planar orbits. We develop a simple analytical model to study the impact of the eccentricity and orbital perturbations on the spin dynamics. This model is relevant in…
Because the distant retrograde orbits dynamics inherently depends on special functions, approximate analytical solutions in the literature are commonly constrained to providing rough approximations of the qualitative behavior. We rely on…
The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…
We propose a method to account for the Earth oblateness effect in preliminary orbit determination of satellites in low orbits with radar observations. This method is an improvement of the one described in (Gronchi et al 2015), which uses a…
The traditional perturbative method is applied to the case of gravitational lensing of planetary systems. A complete and detailed description of the structure of caustics for a system with an arbitrary number of planets can be obtained. I…
We propose a closed-form normalization method suitable for the study of the secular dynamics of small bodies in heliocentric orbits perturbed by the tidal potential of a planet with orbit external to the orbit of the small body. The method…
We present a closed-form normalization method suitable for the study of the secular dynamics of small bodies inside the trajectory of Jupiter. The method is based on a convenient use of a book-keeping parameter introduced not only in the…
While orbital analysis studies were so far mainly focused on the Galactic halo, it is possible now to do these studies in the heavily obscured region close to the Galactic Centre. We aim to do a detailed orbital analysis of stars located in…
Solar radiation pressure can have a substantial long-term effect on the orbits of high area-to-mass ratio spacecraft, such as solar sails. We present a study of the coupling between radiation pressure and the gravitational perturbation due…
Stellar deformations play a significant role in the dynamical evolution of stars in binary systems, impacting the tidal dissipation and the outcomes of mass transfer processes. The prevalent method for modelling the deformations and tidal…
We study the drift of slow variables in a slow-fast Hamiltonian system with several fast and slow degrees of freedom. For any periodic trajectory of the fast subsystem with the frozen slow variables we define an action. For a family of…
We summarize various cases where chaotic orbits can be described analytically. First we consider the case of a magnetic bottle where we have non-resonant and resonant ordered and chaotic orbits. In the sequence we consider the hyperbolic…
In this note we study the generation of attractive oscillations of a class of mechanical systems with underactuation one. The proposed design consists of two terms, i.e., a partial linearizing state feedback, and an immersion and invariance…
We study a class of slow-fast Hamiltonian systems with any finite number of degrees of freedom, but with at least one slow one and two fast ones. At $% \epsilon =0$ the slow dynamics is frozen. We assume that the frozen system (i.e. the…
Applying the method of analytical continuation of periodic orbits, we study quasi-satellite motion in the framework of the three-body problem. In the simplest, yet not trivial model, namely the planar circular restricted problem, it is…
The orbital dynamics of a test particle moving in the non-spherically symmetric field of a rotating oblate primary is impacted also by certain indirect, mixed effects arising from the interplay of the different Newtonian and post-Newtonian…
Compact objects evolving in an astrophysical environment experience a gravitational drag force known as dynamical friction. We present a multipole-frequency decomposition to evaluate the orbit-averaged energy and angular momentum…
Three transiting circumbinary planets (Kepler-16 b, Kepler-34 b, and Kepler-35 b) have recently been discovered from photometric data taken by the Kepler spacecraft. Their orbits are significantly non-Keplerian because of the large…