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We report on a dynamical mean-field theoretical analysis of emerging low-temperature phases in multicomponent gases of fermionic alkaline-earth(-like) atoms in state-dependent optical lattices. Using the example of $^{173}$Yb atoms, we show…
The abstract is additional with repect to the paper published in JGCD. Ordinary Earth satellites are usually placed into five categories of special orbits: sun-synchronous orbits, orbits at the critical inclination, frozen orbits, repeating…
We investigate the behaviour of two recent methods for the computation of preliminary orbits. These methods are based on the conservation laws of Kepler's problem, and enable the linkage of very short arcs of optical observations even when…
In this paper, the general perturbation problem of piecewise smooth integrable differential systems with two switching planes is considered. Firstly, when the unperturbed system has a family of periodic orbits, the first order Melnikov…
Binary systems of two compact objects circularize and spiral toward each other via the emission of gravitational waves. The coupling of the spins of each object with the orbital angular momentum causes the orbital plane to precess, which…
New observational facilities are becoming increasingly capable of observing reflected light from transiting and directly imaged extrasolar planets. In this study, we provide an analytic framework to interpret observed phase curves,…
The case of the classical Hill problem is numerically investigated by performing a thorough and systematic classification of the initial conditions of the orbits. More precisely, the initial conditions of the orbits are classified into four…
In a 2D conservative Hamiltonian system there is a formal integral $\Phi$ besides the energy H. This is not convergent near a stable periodic orbit, but it is convergent near an unstable periodic orbit. We explain this difference and we…
Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…
We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…
We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where…
The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the…
This work explores the dynamic properties of test particles surrounding a distorted, deformed compact object. The astrophysical motivation was to choose such background, which could constitute a more reasonable model of a real situation…
In the framework of multi-body dynamics, successive encounters with a third body, even if well outside of its sphere of influence, can noticeably alter the trajectory of a spacecraft. Examples of these effects have already been exploited by…
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 due to, for example, a variation of the moments of inertia or…
Modeling the orbital dynamics of objects in galactic disks is crucial to understanding the stability and evolution of disk galaxies. While studies of galactic orbits are largely dominated by $N$-body simulations, perturbative analytical…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
We propose a framework for understanding the fragmentation criterion for self-gravitating discs which, in contrast to studies that emphasise the `gravoturbulent' nature of such discs, instead focuses on the properties of their quasi-regular…
This paper presents an analytical model for collision probability assessments between de-orbiting or injecting space objects and satellite constellations. Considering the first to be subjected to a continuous tangential acceleration, its…
The motion of a satellite around a planet can be studied by the Hill model, which is a modification of the restricted three body problem pertaining to motion of a satellite around a planet. Although the dynamics of the circular Hill model…