Siacci’s Theorem for Frenet Curves in Minkowski 3-Space
Yıl: 2020 Cilt: 8 Sayı: 1 Sayfa Aralığı: 159 - 167 Metin Dili: İngilizce DOI: 10.36753/MATHENOT.693053 İndeks Tarihi: 24-03-2021
Siacci’s Theorem for Frenet Curves in Minkowski 3-Space
Öz: For motion of a material point along a space curve, due to Siacci [1], a resolution of the accelerationvector is well known. In this resolution, the acceleration vector is stated as the sum of two special obliquecomponents in the osculating plane to the curve. In this paper, we have studied the Siacci’s theorem fornon-relativistic particles moving along the Frenet curves at very low speeds relative to the speed of lightin Minkowski 3-space. Moreover, an illustrative example is given to show how the aforesaid theoremworks. This theorem is a new contribution to the field and it may be useful for some specific applicationsin theoretical, mathematical and computational physics.
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [1] Siacci, F.: Moto per una linea gobba. Atti R Accad Sci. Torino. 14, 946-951 (1879).
- [2] Babaarslan, M., Yaylı, Y.: On spacelike constant slope surfaces and Bertrand curves in Minkowski 3-space. Annals of the Alexandru Ioan Cuza University-Mathematics (2015). https://doi.org/10.1515/aicu-2015-0009
- [3] Ekici, C., Öztürk, H.: On time-like ruled surfaces in Minkowski 3-space. Universal Journal of Applied Science. 1 (2), 56-63 (2013).
- [4] Lopez, R.: Differential geometry of curves and surfaces in Lorentz-Minkowski space. International Electronic Journal of Geometry. 7 (1), 44-107 (2014).
- [5] Choi, J. H., Kimb, Y. H., Ali, A. T.: Some associated curves of Frenet non-lightlike curves in E3 1 . J. Math. Anal. Appl. 394 (2), 712-723 (2012).
- [6] Altunkaya, B., Kula, L.: Characterizations of slant and spherical helices due to pseudo-Sabban frame. Fundamental Journal of Mathematics and Applications. 1 (1), 49-56 (2018).
- [7] ¸Senyurt, S., Eren, K.: Frenet çatısına göre spacelike normalli spacelike Salkowski e˘grisinden elde edilen Smarandache e ˘grileri. Erzincan Universitesi Fen Bilimleri Enstitüsü Dergisi. 13 (Özel Sayı-I), 7-17 (2020).
- [8] Çetin, E. Ç., Bekta¸s, M.: Some new characterizations of symplectic curve in 4-dimensional symplectic space. Commun. Adv. Math. Sci. 2 (4), 331-334 (2019).
- [9] ¸Senyurt, S., Eren, K.: Spacelike asli normalli spacelike anti-Salkowski E˘grisinin Frenet çatısına göre Smarandache e ˘grileri. Gümü¸shane Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 10 (1), 251-260 (2020).
- [10] Samancı, H. K.: Introduction to timelike uniform B-spline curves in Minkowski-3 space. Journal of Mathematical Sciences and Modelling. 1 (3), 206-210 (2018).
- [11] Eri¸sir, T., Kardag, N. C.: ˜ Spinor representations of involute evolute curves in E3 . Fundam. J. Math. Appl. 2 (2), 148-155 (2019).
- [12] Ersoy, S., Eren, K.: Timelike tangent developable surfaces and Bonnet surfaces. Abstract and Applied Analysis. 2016, 1-7 (2016).
- [13] Tu ˘g, G., Özdemir, Z., Aydın, S. H., Ekmekci, F. N.: Accretive growth kinematics in Minkowski 3-space. International Journal of Geometric Methods in Modern Physics. 14 (05), 1750069 (2017).
- [14] Yıldız, Ö. G., Hızal, S., Akyigit, M.: ˜ Type I + helicoidal surfaces with prescribed weighted mean or Gaussian curvature in Minkowski space with density. An. St. Univ. Ovidius Constanta. 26 (3), 99-108 (2018).
- [15] Siacci, F.: Moto per una linea piana. Atti R Accad Sci. Torino. 14, 750-760 (1879).
- [16] Casey, J.: Siacci’s resolution of the acceleration vector for a space curve. Meccanica. 46 (2), 471-476 (2011).
- [17] Whittaker, E. T.: A Treatise on the analytical dynamics of particles and rigid bodies. Cambridge University Press. New York (1944).
- [18] Grossman, N.: The sheer joy of celestial mechanics. Birkhäuser. Basel (1996).
- [19] Küçükarslan, Z., Yılmaz, M. Y., Bekta¸s, M.: Siacci’s theorem for curves in Finsler manifold F 3 . Turkish Journial of Science and Technology. 7 (2), 181-185 (2012).
- [20] Özen, K. E., Tosun, M., Akyigit, M.: ˜ Siacci’s theorem according to Darboux frame. An. St. Univ. Ovidius Constanta. 25 (3), 155-165 (2017).
- [21] Özen, K. E., Güner, M., Tosun, M.: A note on the acceleration and jerk in motion along a space curve. An. St. Univ. Ovidius Constanta. 28 (1), 151-164 (2020).
APA | Özen K (2020). Siacci’s Theorem for Frenet Curves in Minkowski 3-Space. , 159 - 167. 10.36753/MATHENOT.693053 |
Chicago | Özen Kahraman Esen Siacci’s Theorem for Frenet Curves in Minkowski 3-Space. (2020): 159 - 167. 10.36753/MATHENOT.693053 |
MLA | Özen Kahraman Esen Siacci’s Theorem for Frenet Curves in Minkowski 3-Space. , 2020, ss.159 - 167. 10.36753/MATHENOT.693053 |
AMA | Özen K Siacci’s Theorem for Frenet Curves in Minkowski 3-Space. . 2020; 159 - 167. 10.36753/MATHENOT.693053 |
Vancouver | Özen K Siacci’s Theorem for Frenet Curves in Minkowski 3-Space. . 2020; 159 - 167. 10.36753/MATHENOT.693053 |
IEEE | Özen K "Siacci’s Theorem for Frenet Curves in Minkowski 3-Space." , ss.159 - 167, 2020. 10.36753/MATHENOT.693053 |
ISNAD | Özen, Kahraman Esen. "Siacci’s Theorem for Frenet Curves in Minkowski 3-Space". (2020), 159-167. https://doi.org/10.36753/MATHENOT.693053 |
APA | Özen K (2020). Siacci’s Theorem for Frenet Curves in Minkowski 3-Space. Mathematical Sciences and Applications E-Notes, 8(1), 159 - 167. 10.36753/MATHENOT.693053 |
Chicago | Özen Kahraman Esen Siacci’s Theorem for Frenet Curves in Minkowski 3-Space. Mathematical Sciences and Applications E-Notes 8, no.1 (2020): 159 - 167. 10.36753/MATHENOT.693053 |
MLA | Özen Kahraman Esen Siacci’s Theorem for Frenet Curves in Minkowski 3-Space. Mathematical Sciences and Applications E-Notes, vol.8, no.1, 2020, ss.159 - 167. 10.36753/MATHENOT.693053 |
AMA | Özen K Siacci’s Theorem for Frenet Curves in Minkowski 3-Space. Mathematical Sciences and Applications E-Notes. 2020; 8(1): 159 - 167. 10.36753/MATHENOT.693053 |
Vancouver | Özen K Siacci’s Theorem for Frenet Curves in Minkowski 3-Space. Mathematical Sciences and Applications E-Notes. 2020; 8(1): 159 - 167. 10.36753/MATHENOT.693053 |
IEEE | Özen K "Siacci’s Theorem for Frenet Curves in Minkowski 3-Space." Mathematical Sciences and Applications E-Notes, 8, ss.159 - 167, 2020. 10.36753/MATHENOT.693053 |
ISNAD | Özen, Kahraman Esen. "Siacci’s Theorem for Frenet Curves in Minkowski 3-Space". Mathematical Sciences and Applications E-Notes 8/1 (2020), 159-167. https://doi.org/10.36753/MATHENOT.693053 |