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ON THE CURVATURE THEORY OF NON-NULL CYLINDRICAL SURFACES IN MINKOWSKI 3-SPACE

Yıl 2016, Cilt: 6 Sayı: 1, 22 - 29, 01.06.2016

Öz

This paper presents the curvature theory of non-null cylindrical surfaces in Minkowski 3-space. The de nition of the line of striction and generator trihedron for cylindrical surfaces in Minkowski 3-space are given. The derivation formulae and Darboux instantaneous rotation vectors of generator trihedrons which play important role in robot kinematics are found. Moreover, curvature theory of a Lorentzian circular cylinder is given as an example.

Kaynakça

  • Ayyıldız,N. and Y¨ucesan,A., (2006), On the scalar and dual formulations of the curvature theory of line trajectories in the Lorentzian space, Journal of the Korean Mathematical Society, 43, pp. 1339-1355.
  • Ersoy,S. and Tosun,M., (2008), On the trajectory null scrolls in 3-dimensional Minkowski space-time E31, Kyungpook Math. J., 48, pp. 81-92.
  • Freudenstein,F., (1965), Higher path-curvature analysis in plane kinematics, Journal of Engineering for Industry, 87 (2), pp. 184-190.
  • Kirson,Y., (1975), Curvature theory in space kinematics, Doctoral dissertation, University of Califor- nia, Berkley, Calif, USA.
  • McCarthy,J. M., (1987), On the scalar and dual formulations of curvature theory of line trajectories, Journal of Mechanisms, Transmissions, and Automation in Design, 109 (1), pp. 101106.
  • ONeill,B., (1983), Semi-Riemannian Geometry with Applications to Relativity, Academic Press, Lon- don.
  • ¨Onder,M. and U˘gurlu,H.H., (2013), Frenet frames and invariants of timelike ruled surfaces, Ain Shams Engineering Journal, 4, pp. 507-513.
  • Ratcliffe,J.G., (2006), Foundations of Hyperbolic Manifolds, Springer, New York.
  • Ryuh,B.S., (1989), Robot trajectory planning using the curvature theory of ruled surfaces, Doctoral dissertation, Purdue University, West Lafayette, Ind, USA.
  • Schaaf,J.A., (1988), Curvature theory of line trajectories in spatial kinematics, Doctoral dissertation, University of California, Davis.
  • Struik,D.J., (1950), Lectures on Classical Differential Geometry, Dover Publications, New York.
  • Turgut,A., (1995), 3-Boyutlu Minkowski Uzaynda Spacelike ve Timelike Regle Yzeyler, Doctoral the- sis, Ankara University, Ankara.
  • Beem,J.K. and Ehrlich,P.E., (1981), Global Lorentzian Geometry, Marcel Dekker, New York.
Yıl 2016, Cilt: 6 Sayı: 1, 22 - 29, 01.06.2016

Öz

Kaynakça

  • Ayyıldız,N. and Y¨ucesan,A., (2006), On the scalar and dual formulations of the curvature theory of line trajectories in the Lorentzian space, Journal of the Korean Mathematical Society, 43, pp. 1339-1355.
  • Ersoy,S. and Tosun,M., (2008), On the trajectory null scrolls in 3-dimensional Minkowski space-time E31, Kyungpook Math. J., 48, pp. 81-92.
  • Freudenstein,F., (1965), Higher path-curvature analysis in plane kinematics, Journal of Engineering for Industry, 87 (2), pp. 184-190.
  • Kirson,Y., (1975), Curvature theory in space kinematics, Doctoral dissertation, University of Califor- nia, Berkley, Calif, USA.
  • McCarthy,J. M., (1987), On the scalar and dual formulations of curvature theory of line trajectories, Journal of Mechanisms, Transmissions, and Automation in Design, 109 (1), pp. 101106.
  • ONeill,B., (1983), Semi-Riemannian Geometry with Applications to Relativity, Academic Press, Lon- don.
  • ¨Onder,M. and U˘gurlu,H.H., (2013), Frenet frames and invariants of timelike ruled surfaces, Ain Shams Engineering Journal, 4, pp. 507-513.
  • Ratcliffe,J.G., (2006), Foundations of Hyperbolic Manifolds, Springer, New York.
  • Ryuh,B.S., (1989), Robot trajectory planning using the curvature theory of ruled surfaces, Doctoral dissertation, Purdue University, West Lafayette, Ind, USA.
  • Schaaf,J.A., (1988), Curvature theory of line trajectories in spatial kinematics, Doctoral dissertation, University of California, Davis.
  • Struik,D.J., (1950), Lectures on Classical Differential Geometry, Dover Publications, New York.
  • Turgut,A., (1995), 3-Boyutlu Minkowski Uzaynda Spacelike ve Timelike Regle Yzeyler, Doctoral the- sis, Ankara University, Ankara.
  • Beem,J.K. and Ehrlich,P.E., (1981), Global Lorentzian Geometry, Marcel Dekker, New York.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

B. Şahiner Bu kişi benim

M. Kazaz Bu kişi benim

H. H. Uğurlu Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 6 Sayı: 1

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