Reduction of the semisimple 1:1 resonance |
| |
Authors: | Richard Cushman David L Rod |
| |
Institution: | Mathematics Institute, Rijksuniversiteit Utrecht, Utrecht, The Netherlands;Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada |
| |
Abstract: | The method of “averaging” is often used in Hamiltonian systems of two degrees of freedom to find periodic orbits. Such periodic orbits can be reconstructed from the critical points of an associated “reduced” Hamiltonian on a “reduced space”. This paper details the construction of the reduced space and the reduced Hamiltonian for the semisimple 1:1 resonance case. The reduced space will be a 2-sphere in R3, and the reduced differential equations will be Euler's equations restricted to this sphere. The orbit projection from the energy surface in phase space to this sphere will be the Hopf map. The results of the paper are related to problems in physics on “degeneracies” due to symmetries of classical two-dimensional harmonic oscillators and their quantum analogues for the hydrogen atom. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|