Related papers: Sur la solution de Sundman du probleme des trois c…
The plane case of central configurations with four different masses is analyzed theoretically and is computed numerically. We follow Dziobek's approach to four body central configurations with a direct implicit method of our own in which…
Saari's homographic conjecture, which extends a classical statement proposed by Donald Saari in 1970, claims that solutions of the Newtonian $n$-body problem with constant configurational measure are homographic. In other words, if the…
We consider the classical three-body problem with an arbitrary pair potential which depends on the inter-body distance. A general three-body configuration is set by three "radial" and three angular variables, which determine the shape and…
We show that any bounded zero-angular momentum solution for the Newtonian three-body problem must suffer infinitely many eclipses, or collinearities, provided that it does not suffer a triple collision. Motivation for the result comes from…
In this paper, we consider periodic solutions of the $n$-body problem that satisfy symmetry constraints, expressed through invariance under finite group actions. We focus on their stability properties and present algorithms specifically…
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…
The restricted three body problem is well-known and very important for dynamics of binary, multiple stars and also planetary systems. We extend the classical version of this problem to the situation that there are some external forces from…
A new way for finding analytical solutions of the three-dimensional sine-Gordon equation is presented. The method is based on the established relation between the solutions of the three-dimensional wave equation and solutions of the…
We address the few-body problem using the adiabatic hyperspherical representation. A general form for the hyperangular Green's function in $d$-dimensions is derived. The resulting Lippmann-Schwinger equation is solved for the case of…
A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion. Here we investigate the possibility of partially rigid…
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…
The two body problem in a scalar theory of gravity is investigated. We focus on the closest theory to General Relativity (GR), namely Nordstr\"om's theory of gravity (1913). The gravitational field can be exactly solved for any…
We present a systematically improvable method for numerically solving relativistic three-body integral equations for the partial-wave projected amplitudes. The method consists of a discretization procedure in momentum space, which…
I introduce an extended configuration space for classical mechanical systems, called pair-space, which is spanned by the relative positions of all the pairs of bodies. To overcome the non-independence of this basis, one adds to the…
Continuing work initiated in earlier publications [Ichita, Yamada and Asada, Phys. Rev. D {\bf 83}, 084026 (2011); Yamada and Asada, Phys. Rev. D {\bf 86}, 124029 (2012)], we examine the post-Newtonian (PN) effects on the stability of the…
We explore the three-body problem in two dimensions using the adiabatic hyperspherical representation. We develop the main equations in terms of democratic hyperangular coordinates and determine several symmetry properties and boundary…
This is a very short presentation regarding developments in the theory of nuclear many-body problems, as seen and experienced by the author during the past 60 years with particular emphasis on the contributions of Gerry Brown and his…
Motivated by a problem on the 67th William Lowell Putnam Mathematical Competition, we will summarize three different solutions found on a website. This Putman problem is a special case of Sylvester's four point problem! Suppose four points…
We introduce a circular restricted charged three-body problem on the plane. In this model, the gravitational and Coulomb forces, due to the primary bodies, act on a test particle; the net force exerted by some primary body on the test…
In the present paper, which is a development of an earlier study by the author \cite{Sosnitskii08}, we consider the stability of triangular libration points in the spatial circular restricted three-body problem and improve the result of…