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

YÜCE S., KURUOĞLU N.

Results in Mathematics, cilt.54, sa.1-2, ss.199-206, 2009 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 54 Sayı: 1-2
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1007/s00025-008-0303-7
  • Dergi Adı: Results in Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.199-206
  • Anahtar Kelimeler: Cauchy formula, Enveloping curve, Holditch theorem, Lorentzian motion, Steiner formula
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

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.