Related papers: New Periodic Orbits for the n-Body Problem
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…
The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…
We treat the circular and elliptic restricted three-body problems in inertial frames as periodically forced Kepler problems with additional singularities and explain that in this setting the main result of [4] is applicable. This guarantees…
There are periodic solutions to the equal-mass three-body (and N-body) problem in Newtonian gravity. The figure-eight solution is one of them. In this paper, we discuss its solution in the first and second post-Newtonian approximations to…
The results of an extensive numerical study of the periodic orbits of planar, elliptic restricted three-body planetary systems consisting of a star, an inner massive planet and an outer mass-less body in the external 1:2 mean-motion…
We use the maximally permutation symmetric set of three-body coordinates, that consist of the "hyper-radius" $R = \sqrt{\rho^{2} + \lambda^{2}}$, the "rescaled area of the triangle" $\frac{\sqrt 3}{2 R^2} |{\bm \rho} \times {\bm \lambda}|$)…
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…
In this paper, we prove the existence of a family of new non-collision periodic solutions for the classical Newtonian $n$-body problems. In our assumption, the $n=2l\geq4$ particles are invariant under the dihedral rotation group $D_l$ in…
We present a method for proving the existence of symmetric periodic, heteroclinic or homoclinic orbits in dynamical systems with the reversing symmetry. As an application we show that the Planar Restricted Circular Three Body Problem…
The subject is brake orbits for the 3-body problem: orbits where all velocities are zero at some instant. We extract a paradox and a mystery out of a recent database of 30 non-collision periodic brake orbits for the equal mass 3-body…
We review some recent progress on the research of the periodic orbits of the N-body problem,and propose a numerical scheme to determine the spatial doubly-symmetric periodic orbits (SDSPs for short). Both comet- and lunar-type SDSPs in the…
We numerically discovered around 100 distinct nonrelativistic collisionless periodic three-body orbits in the Coulomb potential in vacuo, with vanishing angular momentum, for equal-mass ions with equal absolute values of charges. These…
In the 70s McGehee introduced a compactification of the phase space of the restricted 3-body problem by gluing a manifold of periodic orbits "at infinity". Although from the dynamical point of view these periodic orbits are parabolic (the…
The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a…
In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…
This paper concerns the restricted 3-body problem. By applying topological methods we give a computer assisted proof of the existence of some classes of periodic orbits, the existence of symbolic dynamics and we give a rigorous lower…
We consider the three body problem on $S^1$ under the cotangent potential. We first construct homothetic orbits ending in singularities, including total collision singularity and collision-antipodal singularity. Then certain symmetrical…
We prove for a large class of n-body problems including a subclass of quasihomogeneous n-body problems, the classical n-body problem, the n-body problem in spaces of negative constant Gaussian curvature and a restricted case of the n-body…
Three-body and n-body problems in celestial mechanics are age-old and challenging puzzles. In recent years, several breakthroughs are made in finding periodic orbits for three-body problem. And Bohua Sun proposed a conjecture on Kepler's…
The planar circular restricted three body problem (PCRTBP) is symmetric with respect to the line of masses and there is a corresponding anti-symplectic involution on the cotangent bundle of the 2-sphere in the regularized PCRTBP. Recently…