Normal forms for the epicyclic approximations of the perturbed Kepler problem |
| |
| Authors: | Giuseppe Pucacco |
| |
| Institution: | Physics Department, University of Rome, “Tor Vergata” and INFN - Sez., Roma II, Italy |
| |
| Abstract: | We compute the normal forms for the Hamiltonian leading to the epicyclic approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian setting corresponds to the dynamics in the Hill synodic system where, by means of the tidal expansion of the potential, the equations of motion take the form of perturbed harmonic oscillators in a rotating frame. In the unperturbed, purely Keplerian case, the post-epicyclic solutions produced with the normal form coincide with those obtained from the expansion of the solution of the Kepler equation. In all cases where the perturbed problem can be cast in autonomous form, the solution is easily obtained as a perturbation series. The generalization to the spatial problem and/or the non-autonomous case is straightforward. |
| |
| Keywords: | Celestial mechanics Planets and satellites: dynamical evolution and stability Methods: analytical |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
