Generalized Hopf fibration and geometric \(\mathrm{SO}(3)\) reduction of the \(4\mathrm{DOF}\) harmonic oscillator

DOI10.1016/S0034-4877(16)30021-0zbMath1411.53074OpenAlexW767765845MaRDI QIDQ1690118

Jan-Cees van der Meer, Francisco Crespo, Sebastián Ferrer

Publication date: 18 January 2018

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(16)30021-0

zbMATH Keywords

symplectic reductionrigid bodyharmonic oscillatorKepler problemHopf fibrationHopf map

Mathematics Subject Classification ID

Momentum maps; symplectic reduction (53D20) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45)

Related Items (2)

The Lissajous-Kustaanheimo-Stiefel transformation ⋮ Reduction and regularization of the Kepler problem

Cites Work

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• On reduction of the four-dimensional harmonic oscillator
• Regularization of kepler's problem and the averaging method on a manifold

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