Cauchy formulas for enveloping curves in the Lorentzian plane and Lorentzian kinematics

YÜCE S., KURUOĞLU N.

Results in Mathematics, vol.54, no.1-2, pp.199-206, 2009 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 1-2
  • 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
  • Keywords: Cauchy formula, Enveloping curve, Holditch theorem, Lorentzian motion, Steiner formula
  • Istanbul Gelisim 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 Yüce and Kuruoǧlu [8] is generalized to three non-collinear points. © 2009 Birkhäuser Verlag Basel/Switzerland.