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

YÜCE S. , Kuruoğlu N.

RESULTS IN MATHEMATICS, cilt.54, ss.199-206, 2009 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 54
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1007/s00025-008-0303-7
  • Sayfa Sayıları: ss.199-206


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.