Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-30853
Saha, P (2009). Interpreting the Kustaanheimo–Stiefel transform in gravitational dynamics. Monthly Notices of the Royal Astronomical Society, 400(1):228-231.
PDF (Accepted manuscript, Version 3)
PDF (Accepted manuscript, Version 2)
PDF (Accepted manuscript, Version 1)
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.
|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Theoretical Physics|
|Uncontrolled Keywords:||stellar dynamics; celestial mechanics|
|Deposited On:||26 Feb 2010 16:18|
|Last Modified:||27 Nov 2013 18:28|
|Additional Information:||The attached file is a preprint (accepted version) of an article published in Monthly Notices of the Royal Astronomical Society. The definitive version is available at www3.interscience.wiley.com|
|Citations:||Web of Science®. Times Cited: 2|
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