50 citations · 572 across the 42 of their papers we have counts for
23 papers · 1 filter
Scaling Symmetries and Conformal Relative Equilibria on Poisson Manifolds, with Applications to Lie--Poisson Systems
Manuele Santoprete
We investigate conformal relative equilibria for Hamiltonian systems on exact Poisson manifolds equipped with scaling symmetries. By introducing conformally Poisson actions and con…
Relative Equilibria for Scaling Symmetries and Central Configurations
Giovanni Rastelli, Manuele Santoprete
In this paper, we explore scaling symmetries within the framework of symplectic geometry. We focus on the action of the multiplicative group on exact symplec…
On the uniqueness of trapezoidal four-body central configurations
Manuele Santoprete
We study central configurations of the Newtonian four-body problem that form a trapezoid. Using a topological argument we prove that there is at most one trapezoidal central config…
On the Uniqueness of Co-circular Four Body Central Configurations
Manuele Santoprete
We study central configurations lying on a common circle in the Newtonian four-body problem. Using a topological argument we prove that there is at most one co-circular central con…
Four-body central configurations with one pair of opposite sides parallel
Manuele Santoprete
We study four-body central configurations with one pair of opposite sides parallel. We use a novel constraint to write the central configuration equations in this special case, usi…
Planarity conditions and four-body central configurations equations with angles as coordinates
Manuele Santoprete
We discuss several conditions for four points to lie on a plane, and we use them to find new equations for four-body central configurations that use angles as variables. We use the…