We apply the analytic-numerical method of Roberts to determine the linear stability of time-
reversible periodic simultaneous binary collision orbits in the symmetric collinear four-body …

We construct a highly-symmetric periodic orbit of eight bodies in three dimensions. In this
orbit, each body collides with its three nearest neighbors in a regular periodic fashion …

We consider the planar symmetric four-body problem with two equal masses m 1= m 3> 0 at
positions (±x 1 (t), 0) and two equal masses m 2= m 4> 0 at positions (0,±x 2 (t)) at all times t …

Abstract We use the Reversibility Error Method and the Fidelity to analyze the global effects
of a small perturbation in a non-integrable system. Both methods have already been …

We apply the symmetry reduction method of Roberts to numerically analyze the linear
stability of a one-parameter family of symmetric periodic orbits with regularizable …

The dynamics of the four-body problem allows for two binary collisions to occur
simultaneously. It is known that in the collinear four-body problem this simultaneous binary …

In this paper, we study the existence and linear stability of the Broucke periodic orbit in the
planar three-body problem. In each period of this orbit, there are two binary collisions (or BC …

Analytical methods are used to prove the existence of a periodic, symmetric solution with
singularities in the planar 4-body problem. Numerical calculation and simulation are used to …

We consider the generalized Sitnikov problem of Newtonian mechanics. For periodic, planar
configurations of n bodies which are symmetric under rotation by a fixed angle, the z-axis is …

We study the rhomboidal symmetric-mass 4-body problem in both a two-degree-of-freedom
and a four-degree-of-freedom setting. Under suitable changes of variables in both settings …