Cauchy Formulas for Enveloping Curves in the Lorentzian Plane and Lorentzian Kinematics

. In the Lorentzian plane, we give Cauchy-length formulas to the envelope of a family of lines. Using these, we prove the length of the enveloping trajectories of non-null lines under the planar Lorentzian motions and give the Holditch-type theorems for the length of the enveloping trajectories. Fur...

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Bibliographic Details
Published in:Resultate der Mathematik 2009-08, Vol.54 (1-2), p.199-206
Main Authors: Yüce, Salim, Kuruoğlu, Nuri
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:. In the Lorentzian plane, we give Cauchy-length formulas to the envelope of a family of lines. Using these, we prove the length of the enveloping trajectories of non-null lines under the planar Lorentzian motions and give the Holditch-type theorems for the length of the enveloping trajectories. Furthermore, Holditch-type theorem for the orbit areas of three collinear points which is given by Yüce and Kuruoğlu [8] is generalized to three non-collinear points.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-008-0303-7