منابع مشابه
Central 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 کاملClassification of four-body central configurations with three equal masses
It is known that a central configuration of the planar four body problem consisting of three particles of equal mass possesses a symmetry if the configuration is convex or is concave with the unequal mass in the interior. We use analytic methods to show that besides the family of equilateral triangle configurations, there are exactly one family of concave and one family of convex central config...
متن کاملCentral Extensions of Supersymmetry in Four and Three Dimensions
We consider the maximal central extension of the supertranslation algebra in d=4 and 3, which includes tensor central charges associated to topological defects such as domain walls (membranes) and strings. We show that for all N -extended superalgebras these charges are related to nontrivial configurations on the scalar moduli space. For N = 2 theories obtained from compactification on Calabi-Y...
متن کاملLectures 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...
متن کاملCentral Configurations and Mutual Differences
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...
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
سال: 2003
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.2002.1061