相关论文: Existence and Stability of Symmetric Periodic Simu…

We apply the analytic-numerical method of Roberts to determine the linear stability of time-reversible periodic simultaneous binary collision orbits in the symmetric collinear four body problem with masses 1, m, m, 1, and also in a…

We apply the symmetry reduction method of Roberts to numerically analyze the linear stability of a one-parameter family of symmetric periodic orbits with regularizable simultaneous binary collisions in the planar pairwise symmetric…

This paper shows the existence of a periodic orbit with singularity in the symmetric collinear four body problem. In each period of the orbit, there is a binary collision (BC) between the inner two bodies and a simultaneous binary collision…

We study orbits near collision in a non-autonomous restricted planar four-body problem. This restricted problem consists of a massless particle moving under the gravitational influence due to three bodies following the figure-eight…

Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily…

We study the rhomboidal symmetric-mass 4-body problem in both a two-degree-of-freedom and a four-degree-of-freedom setting. Under suitable changes of variables in both settings, isolated binary collisions at the origin are regularizable.…

Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…

The dynamics of the 4-body problem allows for two binary collisions to occur simultaneously. It is known that in the collinear 4-body problem this simultaneous binary collision (SBC) can be block-regularised, but that the resulting block…

We consider the planar three body problem of planetary type and we study the generation and continuation of periodic orbits and mainly of asymmetric periodic orbits. Asymmetric orbits exist in the restricted circular three body problem only…

A special 2D initial conditions' domain of the equal-mass zero angular momentum planar three-body problem, which has been formerly studied, is analyzed to deepen the knowledge of the stability regions in it. The decay times in the domain…

We construct a highly-symmetric periodic orbit of six bodies in three dimensions. In this orbit, binary collisions occur at the origin in a regular periodic fashion, rotating between pairs of bodies located on the coordinate axes.…

The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…

We introduce a restricted four body problem in a 2+2 configuration extending the classical Sitnikov problem to the Double Sitnikov problem. The secondary bodies are moving on the same perpendicular line to the planewhere the primaries…

We present a planar four-body model, called the Binary Asteroid Problem, for the motion of two asteroids (having small but positive masses) moving under the gravitational attraction of each other, and under the gravitational attraction of…

In the helium case of the classical Coulomb three-body problem in two dimensions with zero angular momentum, we develop a procedure to find periodic orbits applying two symbolic dynamics for one-dimensional and planar problems. A sequence…

The restricted (equilateral) four-body problem consists of three bodies of masses m1, m2 and m3 (called primaries) lying in a Lagrangian configuration of the three-body problem i.e., they remain fixed at the apices of an equilateral…

We construct a highly-symmetric periodic orbit of eight bodies in three dimensions. In this orbit, each body collides with its three nearest neighbors in a regular periodic fashion. Regularization of the collisions in the orbit is achieved…

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…

We consider the general spatial three body problem and study the dynamics of planetary systems consisting of a star and two planets which evolve into 2/1 mean motion resonance and into inclined orbits. Our study is focused on the periodic…

We study three sub-problems of the N-body problem that have two degrees of freedom, namely the n-pyramidal problem, the planar double-polygon problem, and the spatial double-polygon problem. We prove the existence of several families of…