On the Symmetric Collinear Four-Body Problem

Simultaneous Binary Collisions for Collinear Four-Body Problem

In this paper, we use canonical transformations to collectively analytically continue the singularities of the simultaneous binary collision solutions for the collinear fourbody problem in both the decoupled case and the coupled case. And more importantly, we describe the relationship between the decoupled solutions and the coupled solutions.

Periodic Orbits of a Collinear Restricted Three Body Problem

In this paper we study symmetric periodic orbits of a collinear restricted three body problem, when the middle mass is the largest one. These symmetric periodic orbits are obtained from analytic continuation of symmetric periodic orbits of two collinear two body problems.

Classical Coulomb three-body problem in collinear eZe configuration

Classical dynamics of two-electron atom and ions H−, He, Li, Be, ... in collinear eZe configuration is investigated. It is revealed that the mass ratio ξ between nucleus and electron plays an important role for dynamical behaviour of these systems. With the aid of analytical tool and numerical computation, it is shown that thanks to large mass ratio ξ, classical dynamics of these systems is ful...

Some results on the symmetric doubly stochastic inverse eigenvalue problem

‎The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$‎, ‎to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$‎. ‎If there exists an $ntimes n$ symmetric doubly stochastic ...

Integral equations for the four-body problem