منابع مشابه
Lectures on Central Configurations
These are lecture notes for an advanced course which I gave at the Centre de Recerca Matemàtica near Barcelona in January 2014. The topic is one of my favorites – central configurations of the n-body problem. I gave a course on the same subject in Trieste in 1994 and wrote up some notes (by hand) which can be found on my website [30]. For the new course, I tried to focus on some new ideas and t...
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Central configurations are solutions of the equations λmjqj = ∂U ∂qj , where U denotes the potential function and each qj is a point in the d-dimensional Euclidean space E ∼= R, for j = 1, . . . , n. We show that the vector of the mutual differences qij = qi − qj satisfies the equation − λ αq = Pm(Ψ(q)), where Pm is the orthogonal projection over the spaces of 1-cocycles and Ψ(q) = q |q|α+2 . I...
متن کاملExistence of symmetric central configurations
Central configurations have been of great interest over many years, with the earliest examples due to Euler and Lagrange. There are numerous results in the literature demonstrating the existence of central configurations with specific symmetry properties, using slightly different techniques in each. The aim here is to describe a uniform approach by adapting to the symmetric case the well-known ...
متن کاملCentral Configurations in Three Dimensions
We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in particular as homothetic time-dependent solutions to Newton’s equations of motion and as stationary states in the One Component Plasma model. Concentrating mainly o...
متن کامل6 Se p 20 09 Rosette Central Configurations , Degenerate central configurations and bifurcations
In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian n-body problem. In particular we analyze the Rosette central configurations, namely a coplanar configuration where n particles of mass m1 lie at the vertices of a regular n-gon, n particles of mass m2 lie at the vertices of another n-gon concentric with the first, but rotated of an angle π/n...
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ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2019
ISSN: 0096-3003
DOI: 10.1016/j.amc.2018.10.066