Related papers: Analytical methods in Celestial Mechanics: satelli…
To study the orbits of satellites, a galaxy could be modelled either by means of a static gravitational potential, or by live $N$-body particles. Analytic potentials allow for fast calculations, but are idealized and non-responsive. On the…
The rapid increase in the deployment of Low Earth Orbit (LEO) satellites, catering to diverse applications such as communication, Earth observation, environmental monitoring, and scientific research, has significantly amplified the…
Topical observations of the thermosphere at altitudes below $200 \, km$ are of great benefit in advancing the understanding of the global distribution of mass, composition, and dynamical responses to geomagnetic forcing, and momentum…
Cassini states correspond to equilibria of the spin axis of a body when its orbit is perturbed. They were initially described for satellites, but the spin axis of stars and planets undergoing strong dissipation can also evolve into some…
The theory of the inverse problem is used in order to find a two dimensional galactic potential generating a mono-parametric family of elliptic periodic orbits. The potential is made up of a two-dimensional harmonic oscillator with…
Billiard systems offer a simple setting to study regular and chaotic dynamics. Gravitational billiards are generalizations of these classical billiards which are amenable to both analytical and experimental investigations. Most previous…
To date, studies of $\textit{Laplace Surface}$ dynamics have concerned themselves with test particle orbits of fixed shape and orientation in the combined field of an oblate central body (to which the particle is bound) and a distant,…
The order and chaos of the motion near equilibrium points in the potential of a rotating highly irregular-shaped celestial body are investigated from point of view of the dynamical system theory. The positions of the non-degenerate…
In this paper, we implement a generalised pseudo-Newtonian potential to study the off-equatorial orbits inclined at a certain angle with the equatorial plane around Schwarzschild and Kerr-like compact object primaries surrounded by a…
We provide a constructive method designed in order to control the stability of a given periodic orbit of a general completely integrable system. The method consists of a specific type of perturbation, such that the resulting perturbed…
The traditional way of estimating the gravitational field from observed motions of test objects is based on the virial relation between their kinetic and potential energy. We find a more efficient method. It is based on the natural…
The dynamical evolution of barred galaxies depends crucially on the fraction and their spacial distribution of chaotic orbits in them. In order to distinguish between the two kinds of orbits, we use the Smaller Alignment Index (SALI)…
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
We present a case study for the semiclassical calculation of the oscillations in the particle and kinetic-energy densities for the two-dimensional circular billiard. For this system, we can give a complete classification of all closed…
We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities, also we assume that both planets share the same…
The discovery of multi-planet extrasolar systems has kindled interest in using their orbital evolution as a probe of planet formation. Accurate descriptions of planetary orbits identify systems which could hide additional planets or be in a…
In this paper we present some relevant dynamical properties of an idealized conservative model of the rattleback, from the Poisson dynamics point of view. In the first half of the article, along with a dynamical study of the orbits, using a…
This paper presents a unique approach to the problem of calculating revisit time metrics for different satellite orbits, sensor geometries, and constellation configurations with application to early lifecycle design and optimisation…
In this text we study billiards on ovals and investigate some consequences of a rotational symmetry of the boundary on the dynamics. As it simplifies some calculations, the symmetry helps to obtain the results. We focus on periodic orbits…
New results concerning the orbital stability of periodic traveling wave solutions for the "abcd" Boussinesq model will be shown in this manuscript. For the existence of solutions, we use basic tools of ordinary differential equations to…