Related papers: Analytical methods in Celestial Mechanics: satelli…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
We numerically investigate the orbital dynamics of a two-dimensional galactic model, emphasizing the influence of stable and unstable manifolds on the evolution of orbits. In our analysis we use evaluations of the system's Lagrangian…
We hereby study the stability of a massless probe orbiting around an oblate central body (planet or planetary satellite) perturbed by a third body, assumed to lie in the equatorial plane (Sun or Jupiter for example) using an Hamiltonian…
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 solutions associated with resonant motions, the most important…
We present a computational scheme based on classical molecular dynamics to study chaotic billiards in static external magnetic fields. The method allows to treat arbitrary geometries and several interacting particles. We test the scheme for…
(abbreviated) We use a semi-numerical approach to study the secular behavior of a system composed of a central star and two massive planets in eccentric co-planar orbits. We show that the secular dynamics of this system can be described…
Self-consistent N-body simulations are efficient tools to study galactic dynamics. However, using them to study individual trajectories (or ensembles) in detail can be challenging. Such orbital studies are important to shed light on global…
We have extended the spectral dynamics formalism introduced by Binney & Spergel, and have implemented a semi-analytic method to represent regular orbits in any potential, making full use of their regularity. We use the spectral analysis…
Many exo-solar systems discovered in the last decade consist of planets orbiting in resonant configurations and consequently, their evolution should show long-term stability. However, due to the mutual planetary interactions a multi-planet…
The interval approach to computation of dynamics of celestial bodies in the planetary problem has been considered. It is based on the refusal from idealization of infinitely high resolving capacity of measuring tools, and forms an…
In the present article, we present a new gravitational galactic model, describing motion in elliptical as well as in disk galaxies, by suitably choosing the dynamical parameters. Moreover, a new dynamical parameter, the S(g) spectrum, is…
Starting from the Hamiltonian representation of the dynamics in \cite{rosengren2015chaos,colombo2019long}, this work proposes an innovative procedure to design fully-analytical maneuvers for post-mission disposal of HEOs satellites,…
Dense stellar clusters are natural sites for the origin and evolution of exotic objects such as relativistic binaries (potential gravitational wave sources), blue stragglers, etc. We investigate the secular dynamics of a binary system…
The ordered or chaotic character of orbits of stars moving in the meridional $(R,z)$ plane of an analytic axisymmetric time-independent disk galaxy model with an additional spherically symmetric central nucleus is investigated. Our aim is…
Multiple analytical and empirical stability criteria have been derived in the literature for two planet systems. But, the dependence of the stability limit on the initial mutual inclination between the inner and outer orbits is not well…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
A three-dimensional dynamical model for a galaxy hosting a BL Lacertae object is constructed. The model consists of a logarithmic potential representing an elliptical host galaxy with a bulge of radius $c_b$ and a dense massive nucleus.…
The main objective for this research was the analytical exploration of the dynamics of planar satellite rotation during the motion of an elliptical orbit around a planet. First, we revisit the results of J. Wisdom et al. (1984), in which,…
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 all major perturbations: geopotential at order and degree…
The motion in a simple, time independent rational galactic potential is studied. The potential is a generalization of a two dimensional harmonic oscillator potential and can be considered to describe plane motion in the central parts of a…