相关论文: Synchronised Similar Triangles for Three-Body Orbi…

In this work, we study the periodic orbits in the spatial isosceles three-body problem. These periodic orbits form a one-parameter set with a rotation angle $\theta$ as the parameter. Some new phenomenons are discovered by applying our…

Using the properties of the angular momentum, we develop a new geometrical technique to study relative equilibria for a system of $3$--bodies with positive masses, moving on the two sphere under the influence of an attractive potential…

In this paper, we further investigate the planar Newtonian three-body problem with a focus on collinear configurations, where either the three bodies or their velocities are aligned. We provide an independent proof of Montgomery's result,…

It is shown that nonzero orbital momentum in the vertex of secondary interaction in the triangle graph leads to a more clear picture corresponding to the moving complex singularity compared with the case of constant vertex. The peak in the…

Consider the spatial Newtonian three body problem at fixed negative energy and fixed angular momentum. The moment of inertia $I$ provides a measure of the overall size of a three-body system. We will prove that there is a positive number…

We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…

New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are…

The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle…

Numerical solutions are presented for a family of finite angular momentum orbits with three equal masses which connects the classical circular Lagrange orbit with the recently discovered planar figure eight orbit. Each member of this family…

We present results of numerical calculations showing a three-body orbit's period's $T$ dependence on its topology. This dependence is a simple linear one, when expressed in terms of appropriate variables, suggesting an exact mathematical…

The relative equilibria for the spherical, finite density 3 body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical 5 relative equilibria for the point-mass 3-body…

We present the results of a numerical search for periodic orbits of three equal masses moving in a plane under the influence of Newtonian gravity, with zero angular momentum. A topological method is used to classify periodic three-body…

We consider the 3-body problem in 3-dimensional spaces of nonzero constant Gaussian curvature and study the relationship between the masses of the Lagrangian relative equilibria, which are orbits that form a rigidly rotating equilateral…

The free fall of three particles under Newtonian attraction allows to illustrate some of the complexities of the general three body problem. The total collapse or singularity that occurs when starting from one of the five central…

Suppose that the initial triangle formed by the three moving masses of the three-body problem is similar to the triangle formed at some later time. We derive a simple integral formula for the overall rotation relating the two triangles. The…

We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities, also we assume that both planets share the same…

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…

For three-body problem, R.Montgomery [3] proved a reconstruction formula which calculates the overall rotation relating two similar triangle configurations if the initial triangular configuration is similar to the configuration formed at…

This study presents a study of equilibrium points, periodic orbits, stabilities, and manifolds in a rotating plane symmetric potential field. It has been found that the dynamical behaviour near equilibrium points is completely determined by…

We consider the unrestricted problem of two mutually attracting rigid bodies, an uniform sphere (or a point mass) and an axially symmetric body. We present a global, geometric approach for finding all relative equilibria (stationary…