Planar Central Configuration Estimates in the N-body Problem

نویسنده

  • CHRISTOPHER K. MCCORD
چکیده

For all masses, there are at least n ?2 O 2-orbits of non-collinear planar central conngurations. In particular, this estimate is valid even if the potential function is not a Morse function. If the potential function is a Morse function, then an improved lower bound, on the order of n! ln ? n+1 3 =2, can be given.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Central configurations of the planar coorbital satellite problem

We study the planar central configurations of the 1 + n body problem where one mass is large and the other n masses are infinitesimal and equal. We find analytically all these central configurations when 2 ≤ n ≤ 4. Numerically, first we provide evidence that when n ≥ 9 the only central configuration is the regular n–gon with the large mass in its barycenter, and second we provide also evidence ...

متن کامل

Finiteness of Relative Equilibria in the Planar Generalized N-body Problem with Fixed Subconfigurations

We prove that a fixed configuration of N − 1 masses in the plane can be extended to a central configuration of N masses by adding a specified additional mass only in finitely many ways. This holds for a family of potential functions including the Newtonian gravitational case and the classical planar point vortex model.

متن کامل

Uniqueness Results for Co-Circular Central Configurations for Power-Law Potentials

For a class of potential functions including those used for the planar n-body and n-vortex problems, we investigate co-circular central configurations whose center of mass coincides with the center of the circle containing the bodies. Useful equations are derived that completely describe the problem. Using a topological approach, it is shown that for any choice of positive masses (or circulatio...

متن کامل

Symmetric Planar Central Configurations of Five Bodies: Euler plus Two

We study planar central configurations of the five-body problem where three of the bodies are collinear, forming an Euler central configuration of the three-body problem, and the two other bodies together with the collinear configuration are in the same plane. The problem considered here assumes certain symmetries. From the three bodies in the collinear configuration, the two bodies at the extr...

متن کامل

Convex Four Body Central Configurations with Some Equal Masses

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 quadrilateral and, at most, only one of the remaining masses is larger than the equal masses. Such central configuration posses a symmetry line and it is a kite shaped quadrilateral. We also show that there is exactly on...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1996