Generalized Hopf Fibration and Geometric SO(3) Reduction of the 4DOF Harmonic Oscillator. Issue 2 (April 2016) - van der Meer, J.C.; Crespo, F.; Ferrer, S.
Abstract : It is shown that the generalized Hopf map ℍ × ℍ → ℍ × ℝ × ℝ quaternion formulation can be interpreted as an SO(3) orbit map for a symplectic SO(3) action. As a consequence the generalized Hopf fibration S 7 → S 4 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.