On the existence of collisionless equivariant minimizers for the classical n-body problem

By D. Ferrario, S. Terracini. 2003

240 citations recorded by the source corpus.

We show that the minimization of the Lagrangian action functional on suitable classes of symmetric loops yields collisionless periodic orbits of the n-body problem, provided that some simple conditions on the symmetry group are satisfied. More precisely, we give a fairly general condition on symmetry groups G of the loop space Λ for the n-body problem (with potential of homogeneous degree -α, with α>0) which ensures that the restriction of the Lagrangian action $\mathcal{A}$ to the space ΛG of G-equivariant loops is coercive and its minimizers are collisionless, without any strong force assumption. In proving that local minima of ΛG are free of collisions we develop an averaging technique based on Marchal’s idea of replacing some of the point masses with suitable shapes (see [10]). As an application, several new orbits can be found with some appropriate choice of G. Furthermore, the result can be used to give a simplified and unitary proof of the existence of many already known minimizing periodic orbits.

Subfields: Aerospace Engineering, Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c5ab19c7427b8e4df2f52338ccfab28a525b5ce3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Aerospace Engineering

  1. Xijun Hu
  2. Haiyan Wang
  3. Shanzhong Sun

In Astronomy and Astrophysics

  1. Xijun Hu
  2. Haiyan Wang
  3. Shanzhong Sun

In Statistical and Nonlinear Physics

  1. Pedro J. Torres
  2. Xijun Hu
  3. Meirong Zhang
  4. Haiyan Wang
  5. Shanzhong Sun
  6. Gang Meng

Citations in the corpus