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Equilibrium Points and their stability in the Restricted Four-Body Problem
Numerically the problem of four bodies moving in circles around their center of mass fixed at the origin of the coordinate system, according to the solution of Lagrange where they are always at the vertices of an equilateral triangle, is studied.
Equilibrium points in the photogravitational restricted four-body problem
We study numerically the photogravitational version of the problem of four bodies, where an infinitesimal particle is moving under the Newtonian gravitational attraction of three bodies which are
The stability of vertical motion in the N-body circular Sitnikov problem
We present results about the stability of vertical motion and its bifurcations into families of 3-dimensional (3D) periodic orbits in the Sitnikov restricted N-body problem. In particular, we
Periodic orbits and bifurcations in the Sitnikov four-body problem
We study the existence, linear stability and bifurcations of what we call the Sitnikov family of straight line periodic orbits in the case of the restricted four-body problem, where the three equal
Non-linear stability zones around triangular equilibria in the plane circular restricted three-body problem with oblateness
Non-linear stability zones of the triangular Lagrangian points are computed numerically in the case of oblate larger primary in the plane circular restricted three-body problem. It is found that
Families of periodic orbits in the restricted four-body problem
In this paper, families of simple symmetric and non-symmetric periodic orbits in the restricted four-body problem are presented. Three bodies of masses m1, m2 and m3 (primaries) lie always at the
Analytical solution of the Lagrange quintic equation in the three-body problem in celestial mechanics
SummaryThe Lagrange equation is a quintic (fifth-degree) equation appearing in a stationary solution of the three-body problem in celestial mechanics. This equation has one positive root, which is
Numerical evaluation of analytic functions by Cauchy's theorem
The use of the Cauchy theorem (instead of the Cauchy formula) in complex analysis together with numerical integration rules is proposed for the computation of analytic functions and their derivatives