Generalized Hopf Fibration and Geometric SO(3) Reduction of the 4DOF Harmonic Oscillator. Issue 2 (April 2016)

• Record Type: Journal Article
• Authors: van der Meer, J.C.; Crespo, F.; Ferrer, S.
• Is Part Of: Reports on mathematical physics. Volume 77:Issue 2(2016)
• Page Start: 239
• Page End: 249
• Publication Date: 2016-04
• Subjects: Hopf map -- Hopf fibration -- symplectic reduction -- harmonic oscillator -- Kepler problem -- rigid body; Mathematical physics -- Periodicals; Physique mathématique -- Périodiques; 530.15
• DOI: 10.1016/S0034-4877(16)30021-0
• Languages: English
• ISSNs: 0034-4877

Abstract

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.