Geometrical and physical outlook on the cross product of two quaternions

DOI10.1007/BF01238771zbMath0654.70016MaRDI QIDQ3801127

Maria Dina Vivarelli

Publication date: 1988

Published in: Celestial Mechanics (Search for Journal in Brave)

zbMATH Keywords

Euclidean spacecollisionsaccidental degeneracyKustaanheimo-Stiefel regularizationapplications of quaternions to celestial mechanicscross products of two quaternionselliptical Kepler motionquantum mechanical Kepler problem of the hydrogen atomquaternions space

Mathematics Subject Classification ID

Geometry and quantization, symplectic methods (81S10) Celestial mechanics (70F15)

Related Items

The KS-transformation revisited ⋮ Quaternion methods and models of regular celestial mechanics and astrodynamics ⋮ Invariants of finite and infinite groups generated by reflections ⋮ Linearization: Laplace vs. Stiefel ⋮ On the connection among three classical mechanical problems via the hypercomplex KS-transformation ⋮ Kustaanheimo-Stiefel transformation with an arbitrary defining vector ⋮ The Kepler problem: A unifying view

Cites Work

• The Kepler problem spinor regularization and pre-quantization of the negative-energy manifold
• The KS-transformation in hypercomplex form and the quantization of the negative-energy orbit manifold of the Kepler problem
• An algebraic and geometric approach to non-bijective quadratic transformations
• On the dynamical symmetries of the Kepler problem
• The KS-transformation in hypercomplex form
• Regularization of kepler's problem and the averaging method on a manifold
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