| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 1900301 | Reports on Mathematical Physics | 2016 | 11 Pages |
Abstract
It is shown that the generalized Hopf map ℍ×ℍℍ×ℍ → ℍ×ℝ×ℝℍ×ℝ×ℝquaternion formulation can be interpreted as an SO(3) orbit map for a symplectic SO(3) action. As a consequence the generalized Hopf fibration S7S7 → S4S4 appears in the SO(3) geometric symplectic reduction of the 4DOF isotropic harmonic oscillator. Furthermore it is shown how the Hopf fibration and associated twistor fibration play a role in the geometry of the Kepler problem and the rigid body problem.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
J.C. van der Meer, F. Crespo, S. Ferrer,