Related papers: Probabilistic properties of the elliptic motion
We consider a two-dimensional free harmonic oscillator where the initial position is fixed and the initial velocity can change direction. All possible orbits are ellipses and their enveloping curve is an ellipse too. We show that the locus…
The article presents simple analysis of cones which are used to generate a given conic curve by section by a plane. It was found that if the given curve is an ellipse, then the locus of vertexes of the cones is a hyperbola. The hyperbola…
Based on Propostion 6 of his Principia, Newton's geometrical derivation in Propositions 10 and 11 for the radial dependence of the two central forces that lead to elliptical orbits is notoriously difficult. An alternate and more transparent…
We report first results on elliptic flow of identified particles at mid-rapidity in Au+Au collisions at $\sqrt{s_{_{NN}}}=130$ GeV using the STAR TPC at RHIC. The elliptic flow as a function of transverse momentum and centrality differs…
We present an experimental study of the motion of a circular disk spun onto a table. With the help of a high speed video system, the temporal evolutions of (i) the inclination angle $\alpha$, (ii) the angular velocity $\omega$ and (iii) the…
We develop a theoretical framework for the calculation of orbits for a system consisting of a spherical object and a non-spherical body, which is then specialized to a prolate ellipsoid. Particular trajectories are presented that illustrate…
In this review, we describe the physical processes driving the dynamical evolution of binary stars, namely the circularization of the orbit and the synchronization of their spin and orbital rotation. We also discuss the possible role of the…
Planar run-and-tumble walks with orthogonal directions of motion are considered. After formulating the problem with generic transition probabilities among the orientational states, we focus on the symmetric case, giving general expressions…
The dynamical ellipticity of a planet expresses the departure of its mass distribution from spherical symmetry. It enters as a parameter in the description of a planet's precession and nutation, as well as other rotational normal modes. In…
We study the transition from regular to chaotic motion in a prolate elliptical galaxy dynamical model with a bulge and a dense nucleus. Our numerical investigation shows that stars with angular momentum Lz less than or equal to a critical…
We study independent and identically distributed random iterations of continuous maps defined on a connected closed subset $S$ of the Euclidean space $\mathbb{R}^{k}$. We assume the maps are monotone (with respect to a suitable partial…
In the d dimensional Euclidean space, any set of n+1 independent random points, uniformly distributed in the interior of a unit ball of center O, determines almost surely a circumsphere of center C and of radius R, with n positive and less…
We consider a discrete time particle model for kinetic transport on the two dimensional integer lattice. The particle can move due to advection in the $x$-direction and due to dispersion. This happens when the particle is free, but it can…
We consider the motion of a particle in a random isotropic force field. Assuming that the force field arises from a Poisson field in $\mathbb{R}^d$, $d \geq 4$, and the initial velocity of the particle is sufficiently large, we describe the…
The force acting on a test particle moving around a body that is gravitating and emitting electromagnetic radiation at the same time is computed up to the second order in $1/c$, and the shift of perihelion is found. The total shift is…
A millisecond pulsar having an ellipticity, that is an asymmetric mass distribution around its spin-axis, could emit continuous gravitational waves, which have not been detected so far. An indirect way to infer such waves is to estimate the…
We consider here a generalization of a well known discrete dynamical system produced by the bisection of reflection angles that are constructed recursively between two lines in the Euclidean plane. It is shown that similar properties of…
We propose an analytical method to describe a matter density profile near a galaxy center. The description is based on the study of the distribution function of particles over possible trajectories. We establish a relation between the…
The drag of an elliptic intruder in a two-dimensional granular environment is numerically studied. The movement parallel to the major axis of the intruder is found to be unstable. The drag law is given by the sum of the yield force and the…
The nature of boundedness of orbits of a particle moving in a central force field is investigated. General conditions for circular orbits and their stability are discussed. In a bounded central field orbit, a particle moves clockwise or…