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We describe a simple algorithm for classifying orbits into orbit families. This algorithm works by finding patterns in the sign changes of the principal coordinates. Orbits in the logarithmic potential are studied as an application; we…
The intention of this article is to illustrate the use of methods from symplectic geometry for practical purposes. Our intended audience is scientists interested in orbits of Hamiltonian systems (e.g. the three-body problem). The main…
A class of n-dimensional Poisson systems reducible to an unperturbed harmonic oscillator shall be considered. In such case, perturbations leaving invariant a given symplectic leaf shall be investigated. Our purpose will be to analyze the…
Deep inelastic scattering data on the F_2 structure function provided by the BCDMS, SLAC and NMC collaborations are analyzed in the non-singlet approximation with the analytic and "frozen" modifications of the strong coupling constant…
The discovery of binary and triple asteroids in addition to the execution of space missions to minor celestial bodies in the past several years have focused increasing attention on periodic orbits around irregular-shaped celestial bodies.…
An analytical approximation to periodic orbits in the circular restricted three-body problem is provided. The formulation given in this work is based in calculations known from classical mechanics, but with the addition of the necessary…
We continue our investigation of the bulk properties of asteroid dynamical families identified using only asteroid proper elements (Milani et al. 2014) to provide plausible collisional interpretations. We focus on cratering families…
The problem of orbit flips caused by eccentric von Zeipel-Lidov-Kozai effects is systematically investigated by means of three approaches, including Poincar\'e sections, dynamical system theory (periodic orbits and invariant manifolds) and…
A popular intermediary in the theory of artificial satellites is obtained after the elimination of parallactic terms from the J2-problem Hamiltonian. The resulting quasi-Keplerian system is in turn converted into the Kepler problem by a…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
Using methods from symplectic geometry, the second and fifth authors have provided theoretical groundwork and tools aimed at analyzing periodic orbits, their stability and their bifurcations in families, for the purpose of space mission…
Planets may be rotationally flattened, and their oblateness thus provide useful information on their formation and evolution. Here we develop a new algorithm that can compute the transit light curve due to an oblate planet very efficiently…
In this paper we present a framework which provides an analytical (i.e., infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits…
The structure of the hot downstream region below a radiative accretion shock, such as that of an accreting compact object, may oscillate due to a global thermal instability. The oscillatory behaviour depends on the functional forms of the…
In this article, equilibrium points and families of periodic orbits in the vicinity of the collinear equilibrium points of a binary asteroid system are investigated with respect to the angular velocity of the secondary body, the mass ratio…
The Circular Restricted Three-Body Problem (CR3BP) models the motion of a massless body under the gravitational influence of two primaries. We present a method for approximating a given family of periodic orbits by low-degree implicit…
Broadband dielectric spectroscopy has been performed on single-crystalline FeCr2S4 revealing a transition into a low-temperature orbital glass phase and on polycrystalline FeCr2S4 where long-range orbital order is established via a…
We propose two algorithms to provide a full preliminary orbit of an Earth-orbiting object with a number of observations lower than the classical methods, such as those by Laplace and Gauss. The first one is the Virtual debris algorithm,…
We take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. Due to non-axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends…
In close binary systems, tidal interactions and rotational effects can strongly influence stellar evolution as a result of mass-transfer, common envelope phases, ... All these aspects can only be treated following improvements of…