相关论文: New Periodic Solutions for Some Planar $N+3$-Body …
In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite…
We deal, for the classical $N$-body problem, with the existence of action minimizing half entire expansive solutions with prescribed asymptotic direction and initial configuration of the bodies. We tackle the cases of hyperbolic,…
The Newtonian n-Body Problem is modified assuming positive inertial masses but different sign for the interacting force which is assumed with the possibility of two different signs for the gravitational masses, according to the prescription…
In this paper we address a $n+1$-body gravitational problem governed by the Newton's laws, where $n$ primary bodies orbit on a plane $\Pi$ and an additional massless particle moves on the perpendicular line to $\Pi$ passing through the…
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…
The famous three-body problem can be traced back to Isaac Newton in 1680s. In the 300 years since this "three-body problem" was first recognized, only three families of periodic solutions had been found, until 2013 when \v{S}uvakov and…
In the planar $N$-center problem, for a non-trivial free homotopy class of the configuration space satisfying certain mild condition, we show that there is at least one collision free $T$-periodic solution for any positive $T.$ We use the…
The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more…
The main purpose of this paper is the study of the action that produces Poisson-gradient systems and their multiple periodical solutions. The Section 1 establishes the basic tools. The section 2 underlines conditions in which the action…
Given $n$ point masses turning in a plane at a constant speed, this paper deals with the global bifurcation of periodic solutions for the masses, in that plane and in space. As a special case, one has a complete study of n identical masses…
We revisit the three-body problem in the framework of general relativity. The Newtonian N-body problem admits choreographic solutions, where a solution is called choreographic if every massive particles move periodically in a single closed…
Some properties of the periodic solution of the three-body problem where three particles of equal mass follow the same trajectory are discussed. This trajectory has the shape of a figure-8. The three particles have a constant separation in…
In this work it is shown that there are symmetries beyond the Euclidean group $E\left(3\right)$ in 3-body problem, and by extension in many-body problem, with inverse squared distance inter particle force. The symmetries in 3-body problem…
After the existence proof of the first remarkably stable simple choreographic motion-- the figure eight of the planar three-body problem by Chenciner and Montgomery in 2000, a great number of simple choreographic solutions have been…
We explore variational approach to the finite-volume $N$-body problem. The general formalism for N non-relativistic spinless particles interacting with periodic pair-wise potentials yields N-body secular equations. The solutions depend on…
We prove the existence of periodic solutions of the restricted $(2N+1)$-body problem when the $2N$-primaries move on a periodic Hip-Hop solution and the massless body moves on the line that contains the center of mass and is perpendicular…
We study relativistic Kepler problems in the plane. At first, using non-smooth critical point theory, we show that under a general time-periodic external force of gradient type there are two infinite families of T-periodic solutions,…
Trivial choreographies are special periodic solutions of the planar three-body problem. In this work we use a modified Newton's method based on the continuous analog of Newton's method and a high precision arithmetic for a specialized…
Continuing work initiated in an earlier publication [Ichita, Yamada and Asada, Phys. Rev. D 83, 084026 (2011)], we reexamine the post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem. For three…
We construct a non-perturbative, single-valued solution for the metric and the motion of $N$ interacting particles in $2+1$-Gravity. The solution is explicit for two particles with any speed and for any number of particles with small speed.…