Research Article
Year 2021,
Volume: 3 Issue: 1, 20 - 34, 02.06.2021
Abstract
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.
References
- 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.
Year 2021,
Volume: 3 Issue: 1, 20 - 34, 02.06.2021
Abstract
References
- 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.
There are 17 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Publication Date | June 2, 2021 |
| Acceptance Date | April 5, 2021 |
| Published in Issue | Year 2021 Volume: 3 Issue: 1 |
