BibTex RIS Kaynak Göster

On the invariants of ruled surfaces generated by the dual involute frenet trihedron

Yıl 2017, Cilt: 66 Sayı: 2, 62 - 70, 01.08.2017
https://doi.org/10.1501/Commua1_0000000801

Öz

The purpose of this paper is to describe ruled surfaces generatedby a Frenet trihedron of closed dual involute for a given dual curve. We identifyrelations between the pitch, the angle of the pitch, and the drall of thesesurfaces. Some new results related to the developability of these surfaces arealso obtained. Finally, we illustrate these surfaces by presenting one example

Kaynakça

  • Kücük, A. Gürsoy, O., On the invariants of Bertrand trajectory surface oğsets, App. Math. and Comp. 151 (2004), 763–773.
  • Yang, A. T. and Freudenstein,F., Application of dual-number quaternion algebra to the analysis of spatial mechanisms. J. Appl. Mech. 31 (1964),300–308.
  • Özyilmaz, E. and Yayli, Y., On the integral invariants of a time-like ruled surface, Math. Comput. Appl. 6 (2001), 137–145.
  • Study, E., Geometrie der Dynamen. Verlag Teubner, Leipzig, 1903.
  • Veldkamp, G. R., On the use of dual numbers, vectors, and matrices in instantaneous, spatial kinematics. Mech. and Mach. Theory. 11 (1976), 141–156.
  • Hacısaliho¼glu, H.H., On the pitch of a closed ruled surfaces. Mech. and Mach. Theory. 7 (1972), 291–305 .
  • Hacısaliho¼glu, H.H., MovingGeometry and Quaternion Theory. Publishings of Science and Art Faculty of Gazi University, Ankara-Turkey, 1983.
  • Müller, H. R., Über geschlossene bewegungs vorgange, Monatsh. Math. 55 (1951), 206–214.
  • Gürsoy, O., On the integral invariants of a closed ruled surface, J. of Geom. 39 (1990), 89–91.
  • Gürsoy, O., The dual angle of pitch of a closed ruled surface, Mech. and Mach. Theory. 25 (1990), 131–140.
  • Köse, Ö., Contribution to the theory of integral invariants of a closed ruled surface, Mech. and Mach. Theory. 32 (1997), 261–277.
  • Köse, Ö., Nizamo¼glu, ¸S. and Sezer, M. An explicit characterization of dual spherical curves, Do¼ga Turkish J. Math. 12 (1988), 105–113.
  • Cliğord, W. K. Preliminary sketch of biquaternions. Proc. London Math. Soc. 4 (1873), 381–
  • Yaylı, Y. and Saraço¼glu, S. Ruled surfaces and dual spherical curves, Acta Univ. Apulensis. (2012), 337–354.
  • Current address : Ondokuz Mayıs University, Educational Faculty, Department of Mathematics Atakum, Samsun, TURKEY. E-mail address : mbilici@omu.edu.tr
Yıl 2017, Cilt: 66 Sayı: 2, 62 - 70, 01.08.2017
https://doi.org/10.1501/Commua1_0000000801

Öz

Kaynakça

  • Kücük, A. Gürsoy, O., On the invariants of Bertrand trajectory surface oğsets, App. Math. and Comp. 151 (2004), 763–773.
  • Yang, A. T. and Freudenstein,F., Application of dual-number quaternion algebra to the analysis of spatial mechanisms. J. Appl. Mech. 31 (1964),300–308.
  • Özyilmaz, E. and Yayli, Y., On the integral invariants of a time-like ruled surface, Math. Comput. Appl. 6 (2001), 137–145.
  • Study, E., Geometrie der Dynamen. Verlag Teubner, Leipzig, 1903.
  • Veldkamp, G. R., On the use of dual numbers, vectors, and matrices in instantaneous, spatial kinematics. Mech. and Mach. Theory. 11 (1976), 141–156.
  • Hacısaliho¼glu, H.H., On the pitch of a closed ruled surfaces. Mech. and Mach. Theory. 7 (1972), 291–305 .
  • Hacısaliho¼glu, H.H., MovingGeometry and Quaternion Theory. Publishings of Science and Art Faculty of Gazi University, Ankara-Turkey, 1983.
  • Müller, H. R., Über geschlossene bewegungs vorgange, Monatsh. Math. 55 (1951), 206–214.
  • Gürsoy, O., On the integral invariants of a closed ruled surface, J. of Geom. 39 (1990), 89–91.
  • Gürsoy, O., The dual angle of pitch of a closed ruled surface, Mech. and Mach. Theory. 25 (1990), 131–140.
  • Köse, Ö., Contribution to the theory of integral invariants of a closed ruled surface, Mech. and Mach. Theory. 32 (1997), 261–277.
  • Köse, Ö., Nizamo¼glu, ¸S. and Sezer, M. An explicit characterization of dual spherical curves, Do¼ga Turkish J. Math. 12 (1988), 105–113.
  • Cliğord, W. K. Preliminary sketch of biquaternions. Proc. London Math. Soc. 4 (1873), 381–
  • Yaylı, Y. and Saraço¼glu, S. Ruled surfaces and dual spherical curves, Acta Univ. Apulensis. (2012), 337–354.
  • Current address : Ondokuz Mayıs University, Educational Faculty, Department of Mathematics Atakum, Samsun, TURKEY. E-mail address : mbilici@omu.edu.tr
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Mustafa Bilici

Yayımlanma Tarihi 1 Ağustos 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 66 Sayı: 2

Kaynak Göster

APA Bilici, M. (2017). On the invariants of ruled surfaces generated by the dual involute frenet trihedron. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(2), 62-70. https://doi.org/10.1501/Commua1_0000000801
AMA Bilici M. On the invariants of ruled surfaces generated by the dual involute frenet trihedron. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Ağustos 2017;66(2):62-70. doi:10.1501/Commua1_0000000801
Chicago Bilici, Mustafa. “On the Invariants of Ruled Surfaces Generated by the Dual Involute Frenet Trihedron”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, sy. 2 (Ağustos 2017): 62-70. https://doi.org/10.1501/Commua1_0000000801.
EndNote Bilici M (01 Ağustos 2017) On the invariants of ruled surfaces generated by the dual involute frenet trihedron. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 2 62–70.
IEEE M. Bilici, “On the invariants of ruled surfaces generated by the dual involute frenet trihedron”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 66, sy. 2, ss. 62–70, 2017, doi: 10.1501/Commua1_0000000801.
ISNAD Bilici, Mustafa. “On the Invariants of Ruled Surfaces Generated by the Dual Involute Frenet Trihedron”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/2 (Ağustos 2017), 62-70. https://doi.org/10.1501/Commua1_0000000801.
JAMA Bilici M. On the invariants of ruled surfaces generated by the dual involute frenet trihedron. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:62–70.
MLA Bilici, Mustafa. “On the Invariants of Ruled Surfaces Generated by the Dual Involute Frenet Trihedron”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 66, sy. 2, 2017, ss. 62-70, doi:10.1501/Commua1_0000000801.
Vancouver Bilici M. On the invariants of ruled surfaces generated by the dual involute frenet trihedron. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(2):62-70.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.