42 citations · 82 across the 7 of their papers we have counts for
7 papers
"Twist Vectors" for Central Configuration Equations
Marshall Hampton
A new coordinate system on the tangent space to planar configurations is introduced to simplify some calculations on central configurations and relative equilibria in the -body…
Symmetry and Asymmetry in the 1+N Coorbital Problem
Yiyang Deng, Marshall Hampton, Zhiqiang Wang
The relative equilibria of planar Newtonian -body problem become coorbital around a central mass in the limit when all but one of the masses becomes zero. We prove a variety of…
Equilateral Chains and Cyclic Central Configurations of the Planar 5-body Problem
Yiyang Deng, Marshall Hampton
Central configurations and relative equilibria are an important facet of the study of the -body problem, but become very difficult to rigorously analyze for . In this paper…
Planar -body central configurations with a homogeneous potential
Marshall Hampton
Central configurations give rise to self-similar solutions to the Newtonian -body problem, and play important roles in understanding its complicated dynamics. Even the simple qu…
Constructing and Counting Hexaflexagons
Marshall Hampton
Foldable paper constructions known as flexagons have been studied since 1939. In this paper we review the construction of hexagonal flexagons (hexaflexagons) and compute the number…
Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities
Marshall Hampton, Gareth E. Roberts, Manuele Santoprete
We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, Γ_1 = Γ_2 = 1 and Γ_3 = Γ_4 = m where m is a nonze…
Seven-body central configurations: a family of central configurations in the spatial seven-body problem
Marshall Hampton, Manuele Santoprete
The main result of this paper is the existence of a new family of central configurations in the Newtonian spatial seven-body problem. This family is unusual in that it is a simplex…