Related papers: Collisionless periodic orbits in the free-fall thr…
In this paper we present in detail Newton's method and its modification, based on the Continuous analog of Newton's method for computing periodic orbits of the planar three-body problem. The linear system at each step of the method is…
We consider a one-dimensional system of four inelastic hard spheres, colliding with a fixed restitution coefficient $r$, and we study the inelastic collapse phenomenon for such a particle system. We study a periodic, asymmetric collision…
In this paper we consider periodic orbits of planar linear Filippov systems with a line of discontinuity. Unlike many publications researching only the maximum number of crossing periodic orbits, we investigate not only the number and…
We investigate the motion of a massless body interacting with the Maxwell relative equilibrium, which consists of n bodies of equal mass at the vertices of a regular polygon that rotates around a central mass. The massless body has three…
Three body systems where one of the bodies is ejected without escaping the binary system have previously been studied in various restricted forms. However, none of these studies dwells on the problem in a general setting. Thus, to study…
In the past two decades, since the discovery of the figure-8 orbit by Chenciner and Montgomery, the variational method has became one of the most popular tools for constructing new solutions of the $N$-body problem and its extended…
We present numerical simulations of the gravitational three-body problem, in which three particles lie at rest close to the vertices of an equilateral triangle. In the unperturbed problem, the three particles fall towards the center of mass…
Chaos is present in most stellar dynamical systems and manifests itself through the exponential growth of small perturbations. Exponential divergence drives time irreversibility and increases the entropy in the system. A numerical…
In this work, we perform a first study of basic invariant sets of the spatial Hill's four-body problem, where we have used both analytical and numerical approaches. This system depends on a mass parameter mu in such a way that the classical…
Moore and Montgomery have argued that planar periodic orbits of three bodies moving in the Jacobi-Poincare, or the "strong" pairwise potential $\sum_{i>j}\frac{-1}{r_{ij}^2}$, can have all possible topologies. Here we search systematically…
The quantum version of the free fall problem is a topic often skipped in undergraduate quantum mechanics courses because its discussion usually requires wavepackets built on the Airy functions -- a difficult computation. Here, on the…
We look for particular solutions to the restricted three-body problem where the bodies are allowed to either lose or gain mass to or from a static atmosphere. In the case that all the masses are proportional to the same function of time,we…
In this short exposition, we describe equilibria and periodic orbits in terms of the flow map, {\Phi}, and discuss the essentials of the Jacobian-free Newton-Krylov (JFNK) method that can be used to find them. This method requires little…
We consider a system of four one-dimensional inelastic hard spheres evolving on the real line $\mathbb{R}$, and colliding according to a scattering law characterized by a fixed restitution coefficient $r$. We study the possible orders of…
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…
The continuation of resonant periodic orbits from the restricted to the general three body problem is studied in a systematic way. Starting from the Keplerian unperturbed system we obtain the resonant families of the circular restricted…
We consider the problem of orbital stability of the motion of a test particle in the restricted three-body problem, by using the orbital moment and its time derivative. We show that it is possible to get some insight into the stability…
A periodic orbit on a frictionless billiard table is a piecewise linear path of a billiard ball that begins and ends at the same point with the same angle of incidence. The period of a primitive periodic orbit is the number of times the…
Let a number, N, of particles interact classically through Newton's Laws of Motion and Newton's inverse square Law of Gravitation. The resulting equations of motion provide an approximate mathematical model with numerous applications in…
The Bethe-Salpeter equation for three bosons with zero-range interaction is solved for the first time. For comparison the light-front equation is also solved. The input is the two-body scattering length and the outputs are the three-body…