Gauge symmetry of the N-body problem in the Hamilton–Jacobi approach

@article{Efroimsky2003GaugeSO,
  title={Gauge symmetry of the N-body problem in the Hamilton–Jacobi approach},
  author={Michael Efroimsky and Peter Goldreich},
  journal={Journal of Mathematical Physics},
  year={2003},
  volume={44},
  pages={5958-5977}
}
In most books the Delaunay and Lagrange equations for the orbital elements are derived by the Hamilton–Jacobi method: one begins with the two-body Hamilton equations in spherical coordinates, performs a canonical transformation to the orbital elements, and obtains the Delaunay system. A standard trick is then used to generalize the approach to the N-body case. We reexamine this step and demonstrate that it contains an implicit condition which restricts the dynamics to a 9(N–1)-dimensional… 

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