Quaternions for regularizing celestial mechanics: The right way

DOI10.1007/s10569-008-9124-yzbMath1154.70309OpenAlexW2150749878MaRDI QIDQ1003172

Jörg Waldvogel

Publication date: 27 February 2009

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11850/69851

zbMATH Keywords

RegularizationBirkhoff transformationPerturbed Kepler problemQuaternionsQuaternion algebraJoukowsky-Birkhoff mappingKepler formulasKustaanheimo-Stiefel transformation

Mathematics Subject Classification ID

Two-body problems (70F05) Celestial mechanics (70F15)

Related Items (15)

Quasi‐Periodic Almost‐Collision Orbits in the Spatial Three‐Body Problem ⋮ Regular quaternion models of perturbed orbital motion of a rigid body in the Earth's gravitational field ⋮ Quaternion methods and models of regular celestial mechanics and astrodynamics ⋮ Asymptotic solution for the two-body problem with constant tangential thrust acceleration ⋮ Continuation of equilibria and stability of slender elastic rods using an asymptotic numerical method ⋮ -invariants for planar two-center Stark–Zeeman systems ⋮ Conformal transformations and integrable mechanical billiards ⋮ Perturbed spatial two-body problem: regular quaternion equations of relative motion ⋮ Alternative angle-based approach to the \(\mathcal{KS}\)-map. An interpretation through symmetry and reduction ⋮ Kustaanheimo-Stiefel transformation with an arbitrary defining vector ⋮ A global regularisation for integrating the Caledonian symmetric four-body problem ⋮ Parametric quartic Hamiltonian model. A unified treatment of classic integrable systems ⋮ Kustaanheimo-Stiefel regularization and the quadrupolar conjugacy ⋮ The spatial \(N\)-centre problem: scattering at positive energies ⋮ PERTURBED KEPLER PROBLEM IN GENERAL RELATIVITY WITH QUATERNIONS

Cites Work

• Quaternions and the perturbed Kepler problem
• Quaternions and the rotation of a rigid body
• Singularities in gravitational systems. Applications to chaotic transport in the solar system
• Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche
• Perturbed Kepler problem in quaternionic form
• The KS-transformation in hypercomplex form
• Perturbation theory of Kepler motion based on spinor regularization.
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