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Interpreting the Kustaanheimo-Stiefel transform in gravitational dynamics

Saha, Prasenjit

In: Monthly Notices of the Royal Astronomical Society, 2009, vol. 400, no. 1, p. 228-231

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    Titre
    • Interpreting the Kustaanheimo-Stiefel transform in gravitational dynamics
    Auteur
    • Saha, Prasenjit. Institute for Theoretical Physics, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
    Type de document
    • Postprint
    Langue
    • Inglese
    Publié dans
    • Monthly Notices of the Royal Astronomical Society, 2009, vol. 400, no. 1, p. 228-231. Blackwell Publishing Ltd
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:292584
    Summary
    The Kustaanheimo-Stiefel (KS) transform turns a gravitational two-body problem into a harmonic oscillator, by going to four dimensions. In addition to the mathematical-physics interest, the KS transform has proved very useful in N-body simulations, where it helps to handle close encounters. Yet the formalism remains somewhat arcane, with the role of the extra dimension being especially mysterious. This paper shows how the basic transformation can be interpreted as a rotation in three dimensions. For example, if we slew a telescope from zenith to a chosen star in one rotation, we can think of the rotation axis and angle as the KS transform of the star. The non-uniqueness of the rotation axis encodes the extra dimension. This geometrical interpretation becomes evident on writing KS transforms in quaternion form, which also helps to derive concise expressions for regularized equations of motion