Araştırma Makalesi
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A New Moving Frame for Trajectories on Regular Surfaces

Yıl 2021, Cilt: 3 Sayı: 1, 20 - 34, 02.06.2021

Öz

In this study, we introduce a new moving frame on regular surfaces for trajectories with non-vanishing angular momentum and give the angular velocity vector for this frame. Then, we consider the special trajectories generated by Smarandache curves according to this frame in three-dimensional Euclidean space and investigate the Serret-Frenet apparatus of them. Moreover, we provide an illustrative example explaining how this frame is constructed and how the aforementioned special trajectories are generated. This moving frame is a new contribution to the field and we expect that it will be useful in some specific applications of differential geometry and kinematics in the future.

Kaynakça

  • Ali, A. T. (2010) Special Smarandache curves in the Euclidian space. International J. Math. Combin., 2:30-36.
  • Altunkaya, B., Aksoyak, F. K. (2017) Curves of constant breadth according to Darboux frame. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(2):44-52.
  • Bektas¸, Ö., Yüce, S. (2013) Smarandache curves according to Darboux frame in E3. Romanian Journal of Mathematics and Computer Science, 3(1):48-59.
  • Casey, J. (2011) Siacci’s resolution of the acceleration vector for a space curve. Meccanica, 46:471-476.
  • Çetin, M., Tuncer, Y., Karacan, M. K. (2014) Smarandache curves according to Bishop frame in Euclidean 3-space. Gen. Math. Notes, 20:50-66.
  • Doğan, F., Yaylı, Y. (2012) Tubes with Darboux frame. Int. J. Contemp. Math. Sciences, 7(16):751-758.
  • Kızıltuğ, S., Yaylı, Y. (2013) Timelike tubes with Darboux frame in Minkowski 3-space. International Journal of Physical Sciences, 8(1):31-36.
  • Körpınar, T., Ünlütürk, Y. (2020) An approach to energy and elastic for curves with extended Darboux frame in Minkowski space. AIMS Mathematics, 5(2):1025-1034.
  • O’Neil, B. (1966) Elemantary differential geometry. Academic Press, Newyork.
  • Özen, K. E., Tosun, M., Akyiğit, M. (2017) Siacci’s theorem according to Darboux frame. Analele Universitatii Ovidius Constanta-Seria Matematica, 25(3):155-165.
  • Radzevich, S. P. (2013) Geometry of surfaces: A practical guide for mechanical engineers. Wiley.
  • Shifrin, T. (2008) Differential geometry: A first course in curves and surfaces. University of Georgia, Preliminary Version.
  • Şentürk, G. Y., Yüce, S. (2017) Bertrand offsets of ruled surfaces with Darboux frame. Results in Mathematics, 72(3):1151-1159.
  • Şenyurt, S., Eren, K. (2020) Smarandache curves of spacelike anti-Salkowski curve with a spacelike principal normal according to Frenet frame. Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 10(1):251-260.
  • Taşköprü, K., Tosun, M. (2014) Smarandache curves on S2. Boletim da Sociedade Paranaense de Matematica, 32(1):51-59.
  • Tosun, M., Hızarcıoğlu, M. (2020) On the jerk in motion along a regular surface curve. In: Hvedri, I. (ed.) TBILISI-MATHEMATICS (pp. 67-75). Sciendo, Berlin.
  • Turgut, M., Yılmaz, S. (2008) Smarandache curves in Minkowski space-time. International J. Math. Combin.,3:51-55.
Yıl 2021, Cilt: 3 Sayı: 1, 20 - 34, 02.06.2021

Öz

Kaynakça

  • Ali, A. T. (2010) Special Smarandache curves in the Euclidian space. International J. Math. Combin., 2:30-36.
  • Altunkaya, B., Aksoyak, F. K. (2017) Curves of constant breadth according to Darboux frame. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(2):44-52.
  • Bektas¸, Ö., Yüce, S. (2013) Smarandache curves according to Darboux frame in E3. Romanian Journal of Mathematics and Computer Science, 3(1):48-59.
  • Casey, J. (2011) Siacci’s resolution of the acceleration vector for a space curve. Meccanica, 46:471-476.
  • Çetin, M., Tuncer, Y., Karacan, M. K. (2014) Smarandache curves according to Bishop frame in Euclidean 3-space. Gen. Math. Notes, 20:50-66.
  • Doğan, F., Yaylı, Y. (2012) Tubes with Darboux frame. Int. J. Contemp. Math. Sciences, 7(16):751-758.
  • Kızıltuğ, S., Yaylı, Y. (2013) Timelike tubes with Darboux frame in Minkowski 3-space. International Journal of Physical Sciences, 8(1):31-36.
  • Körpınar, T., Ünlütürk, Y. (2020) An approach to energy and elastic for curves with extended Darboux frame in Minkowski space. AIMS Mathematics, 5(2):1025-1034.
  • O’Neil, B. (1966) Elemantary differential geometry. Academic Press, Newyork.
  • Özen, K. E., Tosun, M., Akyiğit, M. (2017) Siacci’s theorem according to Darboux frame. Analele Universitatii Ovidius Constanta-Seria Matematica, 25(3):155-165.
  • Radzevich, S. P. (2013) Geometry of surfaces: A practical guide for mechanical engineers. Wiley.
  • Shifrin, T. (2008) Differential geometry: A first course in curves and surfaces. University of Georgia, Preliminary Version.
  • Şentürk, G. Y., Yüce, S. (2017) Bertrand offsets of ruled surfaces with Darboux frame. Results in Mathematics, 72(3):1151-1159.
  • Şenyurt, S., Eren, K. (2020) Smarandache curves of spacelike anti-Salkowski curve with a spacelike principal normal according to Frenet frame. Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 10(1):251-260.
  • Taşköprü, K., Tosun, M. (2014) Smarandache curves on S2. Boletim da Sociedade Paranaense de Matematica, 32(1):51-59.
  • Tosun, M., Hızarcıoğlu, M. (2020) On the jerk in motion along a regular surface curve. In: Hvedri, I. (ed.) TBILISI-MATHEMATICS (pp. 67-75). Sciendo, Berlin.
  • Turgut, M., Yılmaz, S. (2008) Smarandache curves in Minkowski space-time. International J. Math. Combin.,3:51-55.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Kahraman Esen Özen 0000-0002-3299-6709

Murat Tosun 0000-0002-4888-1412

Yayımlanma Tarihi 2 Haziran 2021
Kabul Tarihi 5 Nisan 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 3 Sayı: 1

Kaynak Göster

APA Özen, K. E., & Tosun, M. (2021). A New Moving Frame for Trajectories on Regular Surfaces. Ikonion Journal of Mathematics, 3(1), 20-34.
AMA Özen KE, Tosun M. A New Moving Frame for Trajectories on Regular Surfaces. ikjm. Haziran 2021;3(1):20-34.
Chicago Özen, Kahraman Esen, ve Murat Tosun. “A New Moving Frame for Trajectories on Regular Surfaces”. Ikonion Journal of Mathematics 3, sy. 1 (Haziran 2021): 20-34.
EndNote Özen KE, Tosun M (01 Haziran 2021) A New Moving Frame for Trajectories on Regular Surfaces. Ikonion Journal of Mathematics 3 1 20–34.
IEEE K. E. Özen ve M. Tosun, “A New Moving Frame for Trajectories on Regular Surfaces”, ikjm, c. 3, sy. 1, ss. 20–34, 2021.
ISNAD Özen, Kahraman Esen - Tosun, Murat. “A New Moving Frame for Trajectories on Regular Surfaces”. Ikonion Journal of Mathematics 3/1 (Haziran 2021), 20-34.
JAMA Özen KE, Tosun M. A New Moving Frame for Trajectories on Regular Surfaces. ikjm. 2021;3:20–34.
MLA Özen, Kahraman Esen ve Murat Tosun. “A New Moving Frame for Trajectories on Regular Surfaces”. Ikonion Journal of Mathematics, c. 3, sy. 1, 2021, ss. 20-34.
Vancouver Özen KE, Tosun M. A New Moving Frame for Trajectories on Regular Surfaces. ikjm. 2021;3(1):20-34.