Mathematics – Complex Variables
Scientific paper
Jan 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..29...45v&link_type=abstract
Celestial Mechanics (ISSN 0008-8714), vol. 29, Jan. 1983, p. 45-50. Research supported by the Consiglio Nazionale delle Ricerche
Mathematics
Complex Variables
14
Celestial Mechanics, Complex Variables, Gauge Theory, Kepler Laws, Quaternions, Transformations (Mathematics), Identities, Matrices (Mathematics)
Scientific paper
In this note the KS-transformation introduced by Kustaanheimo and Stiefel into Celestial Mechanics is formulated in terms of hypercomplex numbers as the product of a quaternion and its anti-involute. Therefore it represents a particular morphism of the real algebra of quaternions - having for image a three-dimensional real linear subspace - and also a natural generalization of the Levi-Civita transformation. The quaternion matrix of the product leads to the KS-matrix; the bilinear relation and the two identities which play a central role in the KS-theory are easily derived. A suitable quaternion gauge-transformation is given which leads to the well-known fibration of the four-dimensional space. In addition several geometrical interpretations are brought out.
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