19 citations · 40 across the 4 of their papers we have counts for
5 papers
On Kite Central Configurations
Gareth E. Roberts
We study kite central configurations in the Newtonian four-body problem. We present a new proof that there exists a unique convex kite central configuration for a given choice of p…
Classifying Four-Body Convex Central Configurations
Montserrat Corbera, Josep M. Cors, Gareth E. Roberts
We classify the full set of convex central configurations in the Newtonian four-body problem. Particular attention is given to configurations possessing some type of symmetry or de…
Morse Theory and Relative Equilibria in the Planar -Vortex Problem
Gareth E. Roberts
Morse theoretical ideas are applied to the study of relative equilibria in the planar -vortex problem. For the case of positive circulations, we prove that the Morse index of a…
Existence and Stability of Four-Vortex Collinear Relative Equilibria with Three Equal Vorticities
Brian Menezes, Gareth E. Roberts
We study collinear relative equilibria of the planar four-vortex problem where three of the four vortex strengths are identical. The invariance obtained from the equality of…
A Four-Body Convex Central Configuration with Perpendicular Diagonals Is Necessarily a Kite
Montserrat Corbera, Josep M. Cors, Gareth E. Roberts
We prove that any four-body convex central configuration with perpendicular diagonals must be a kite configuration. The result extends to general power-law potential functions, inc…