The Axisymmetric Central Configurations of the Four-Body Problem with Three Equal Masses

  title={The Axisymmetric Central Configurations of the Four-Body Problem with Three Equal Masses},
  author={Emese Kov{\'a}ri and B{\'a}lint {\'E}rdi},
In the studied axisymmetric case of the central four-body problem, the axis of symmetry is defined by two unequal-mass bodies, while the other two bodies are situated symmetrically with respect to this axis and have equal masses. Here, we consider a special case of the problem and assume that three of the masses are equal. Using a recently found analytical solution of the general case, we formulate the equations of condition for three equal masses analytically and solve them numerically. A… 

Figures from this paper

Symmetries in Stellar, Galactic, and Extragalactic Astronomy
Examples are presented for appearance of geometric symmetry in the shape of various astronomical objects and phenomena. Usage of these symmetries in astrophysical and extragalactic research is also


Central configurations of four bodies with an axis of symmetry
A complete solution is given for a symmetric case of the problem of the planar central configurations of four bodies, when two bodies are on an axis of symmetry, and the other two bodies have equal
On the role and the properties ofn body central configurations
The role central configurations play in the analysis ofn body systems is outlined. Emphasis is placed on collision orbits, expanding gravitational systems, andn body ‘zero radial velocity’ surfaces.
Four-Body Central Configurations¶with some Equal Masses
Abstract We prove firstly that any convex non-collinear central configuration of the planar 4-body problem with equal opposite masses β >α > 0, such that the diagonal corresponding to the mass α is
Relative equilibrium solutions in the four body problem
Beyond the casen=3 little was known about relative equilibrium solutions of then-body problem up to recent years. Palmore's work provides in the general case much useful information. In the casen=4
Bifurcations of relative equilibria in the 4- and 5-body problem
Abstract The equilateral triangle family of relative equilibria of the 4-body problem consists of three particles of mass 1 at the vertices of an equilateral triangle and the fourth particle of
Classifying relative equilibria. III
We announce several theorems on the evolution of relative equilibria classes in the planar n-body problem. In an earlier paper [1] we announced a partial classification of relative equilibria of four
On the planar central configurations of the 4-body problem with three equal masses
  • Math. Anal.
  • 2009
The symmetric central configurations of four equal masses
  • Commun. Contemp. Math.
  • 1996
Topology and mechanics. II