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

YÜCE S., Kuruoğlu N.

RESULTS IN MATHEMATICS, vol.54, pp.199-206, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54
  • Publication Date: 2009
  • Doi Number: 10.1007/s00025-008-0303-7
  • Journal Name: RESULTS IN MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.199-206
  • Yıldız Technical University Affiliated: Yes

Abstract

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 Yuce and Kuruoglu [8] is generalized to three non-collinear points.