50 citations · 572 across the 42 of their papers we have counts for
13 papers · 2 filters
Smoothed dynamics in the central field problem
Manuele Santoprete, Cristina Stoica
Consider the motion of a material point of unit mass in a central field determined by a homogeneous potential of the form , where being the distance to the cen…
Saari's Homographic Conjecture of the Three-Body Problem
Florin Diacu, Toshiaki Fujiwara, Ernesto Perez-Chavela +1
Saari's homographic conjecture, which extends a classical statement proposed by Donald Saari in 1970, claims that solutions of the Newtonian -body problem with constant configur…
Central Configurations and Total Collisions for Quasihomogeneous n-Body Problems
Florin Diacu, Ernesto Perez-Chavela, Manuele Santoprete
We consider -body problems given by potentials of the form with constants, . To analyze the dynamics of the problem, we first pro…
Saari's Conjecture for the Collinear -Body Problem
Florin Diacu, Ernesto Perez-Chavela, Manuele Santoprete
In 1970 Don Saari conjectured that the only solutions of the Newtonian -body problem that have constant moment of inertia are the relative equilibria. We prove this conjecture i…
Linear stability of the Lagrangian triangle solutions for quasihomogeneous potentials
Manuele Santoprete
In this paper we study the linear stability of the relative equilibria for homogeneous and quasihomogeneous potentials. Firstly, in the case the potential is a homogeneous function…
The Kepler Problem with Anisotropic Perturbations
Florin Diacu, Ernesto Perez-Chavela, Manuele Santoprete
We study a 2-body problem given by the sum of the Newtonian potential and an anisotropic perturbation that is a homogeneous function of degree , . For , the sets o…
A Counterexample to a Generalized Saari's Conjecture with a Continuum of Central Configurations
Manuele Santoprete
In this paper we show that in the -body problem with harmonic potential one can find a continuum of central configurations for . Moreover we show a counterexample to an int…
Rosette Central Configurations, Degenerate central configurations and bifurcations
Jinzhi Lei, Manuele Santoprete
In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian -body problem. In particular we analyze the Rosette central configuratio…
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…
Convex Four Body Central Configurations with Some Equal Masses
Ernest Perez-Chavela, Manuele Santoprete
We prove that there is a unique convex non-collinear central configuration of the planar Newtonian four-body problem when two equal masses are located at opposite vertices of a qua…
Escape dynamics in collinear atomic-like three mass point systems
Daniel Pasca, manuele Santoprete, Cristina Stoica
The present paper studies the escape mechanism in collinear three point mass systems with small-range-repulsive/large-range-attractive pairwise-interaction. Specifically, we focus…
Block regularization of the Kepler problem on surfaces of revolution with positive constant curvature
Manuele Santoprete
We consider the Kepler problem on surfaces of revolution that are homeomorphic to and have constant Gaussian curvature. We show that the system is maximally superintegrable,…
Central Configurations of the Five-Body Problem with Equal Masses
Tsung-Lin Lee, Manuele Santoprete
In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses. This is accomplished by using the polyhedral h…