50 citations · 572 across the 42 of their papers we have counts for
43 papers
The Hessian of Planar Central Configurations in Pair Space: Decomposition, Morse Index and Symmetry Reduction
Manuele Santoprete
We give a variational derivation of the central configuration equations in pair space, where the relative position vectors between pairs of bodies serve as the primary variables. V…
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…
Some Polynomial Conditions of Cyclic Quadrilaterals, Tilted Kites and Other Quadrilaterals
Manuele Santoprete
In this paper, we investigate some polynomial conditions that arise from Euclidean geometry. First we study polynomials related to quadrilaterals with supplementary angles, this in…