Araştırma Makalesi
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Yıl 2023, Cilt: 72 Sayı: 1, 216 - 228, 30.03.2023

Zehra İşbilir Kahraman Esen Özen Murat Tosun

https://doi.org/10.31801/cfsuasmas.1094170

Öz

Kaynakça

  • Bertrand, J., Memoire sur la theorie des courbes `a double courbure, J. Math. Pures Appl., (1850) 332–350.
  • Bishop, R. L., There is more than one way to frame a curve, Amer. Math. Monthly, 82(3) (1975) 246–251. https://doi.org/10.2307/2319846
  • Burke, J. F., Bertrand curves associated with a pair of curves, Math. Mag., 34(1) (1960), 60–62. https://doi.org/10.2307/2687860
  • Casey, J., Siacci’s resolution of the acceleration vector for a space curve, Meccanica, 46 (2011), 471–476. https://doi.org/10.1007/s11012-010-9296-x
  • da Silva, L. C., Differential Geometry of Rotation Minimizing Frames, Spherical Curves, and Quantum Mechanics of a Constrained Particle, Ph.D Thesis, 2017, (2018), arXiv preprint, arXiv:1806.08830.
  • Darboux, G., Le¸cons Sur La Theorie Generale Des Surfaces I-II-III-IV, Gauthier Villars, Paris, 1896.
  • Dede, M., Ekici, C., Directional Bertrand curves, Gazi Univ. J. Sci., 31(1) (2018), 202–211.
  • Dede, M., Aslan, M. Ç., Ekici, C., On a variational problem due to the B-Darboux frame in Euclidean 3-space, Math. Methods Appl. Sci., 44(17) (2021), 12630–12639. https://doi.org/10.1002/mma.7567
  • Goldstein, H., Poole, C. P., Safko, J. L., Classical Mechanics, Vol. 2, Reading, MA: Addison-Wesley, 1950.
  • Görgülü, A., A generalization of the Bertrand curves as general inclined curves in $E^n$, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 35(01.02) (1986), 54–60. https://doi.org/10.1501/Commua1 0000000254
  • Gürbüz, N. E., The evolution of an electric field with respect to the type-1 PAF and the PAFORS frames in $R^3_1$, Optik, 250(1) (2022), 168285. https://doi.org/10.1016/j.ijleo.2021.168285
  • Izumiya, S., Takeuchi, N., Generic properties of helices and Bertrand curves, J. Geom., 74 (2002), 97–109. https://doi.org/10.1007/PL00012543
  • İlarslan, K., Nesovic, E., Some characterizations of osculating curves in the Euclidean spaces, Demonstr. Math., 41(4) (2008), 931–939. https://doi.org/10.1515/dema-2008-0421
  • Kazaz, M., Uğurlu, M. M., Önder, M., Oral, S., Bertrand partner D-curves in the Euclidean 3-space $E^3$, Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, 16(1) (2016), 76–83. https://doi.org/10.5578/fmbd.25270
  • Özen, K. E., Tosun, M., A new moving frame for trajectories with non-vanishing angular momentum, J. Math. Sci. Model., 4(1) (2021), 7–18. https://doi.org/10.33187/jmsm.869698
  • Özen, K. E., Tosun, M., Trajectories generated by special Smarandache curves according to Positional Adapted Frame, Karamanoğlu Mehmetbey University Journal of Engineering and Natural Sciences, 3(1) (2021), 15–23.
  • Papaioannou, S. G., Kiritsis, D., An application of Bertrand curves and surfaces to CADCAM, Computer-Aided Design, 17(8) (1985), 348–352. https://doi.org/10.1016/0010-4485(85)90025-9
  • Shifrin T., Differential Geometry: A First Course in Curves and Surfaces, University of Georgia, Preliminary Version, 2008.
  • Solouma, E. M., Characterization of Smarandache trajectory curves of constant mass point particles as they move along the trajectory curve via PAF, Bulletin of Mathematical Analysis and Applications, 13(4) (2021), 14–30. https://doi.org/10.54671/bmaa-2021-4-2
  • Whittemore, J. K., Bertrand curves and helices, Duke Math. J., 6(1) (1940), 235–245. https://doi.org/10.1215/S0012-7094-40-00618-4
  • Yerlikaya, F., Karaahmetoğlu, S., Aydemir, İ., On the Bertrand B-pair curve in 3-dimensional Euclidean space, Journal of Science and Arts, 3(36) (2016), 215–224.

Bertrand partner P-trajectories in the Euclidean 3-space $E^3$

Yıl 2023, Cilt: 72 Sayı: 1, 216 - 228, 30.03.2023

Zehra İşbilir Kahraman Esen Özen Murat Tosun

https://doi.org/10.31801/cfsuasmas.1094170

Öz

The concept of a pair of curves, called as Bertrand partner curves, was introduced by Bertrand in 1850. Bertrand partner curves have been studied widely in the literature from past to present. In this study, we take into account of the concept of Bertrand partner trajectories according to Positional Adapted Frame (PAF) for the particles moving in 3-dimensional Euclidean space. Some characterizations are given for these trajectories with the aid of the PAF elements. Then, we obtain some special cases of these trajectories. Moreover, we provide a numerical example.

Anahtar Kelimeler

Kinematics of a particle Bertrand curves positional adapted frame

Kaynakça

  • Bertrand, J., Memoire sur la theorie des courbes `a double courbure, J. Math. Pures Appl., (1850) 332–350.
  • Bishop, R. L., There is more than one way to frame a curve, Amer. Math. Monthly, 82(3) (1975) 246–251. https://doi.org/10.2307/2319846
  • Burke, J. F., Bertrand curves associated with a pair of curves, Math. Mag., 34(1) (1960), 60–62. https://doi.org/10.2307/2687860
  • Casey, J., Siacci’s resolution of the acceleration vector for a space curve, Meccanica, 46 (2011), 471–476. https://doi.org/10.1007/s11012-010-9296-x
  • da Silva, L. C., Differential Geometry of Rotation Minimizing Frames, Spherical Curves, and Quantum Mechanics of a Constrained Particle, Ph.D Thesis, 2017, (2018), arXiv preprint, arXiv:1806.08830.
  • Darboux, G., Le¸cons Sur La Theorie Generale Des Surfaces I-II-III-IV, Gauthier Villars, Paris, 1896.
  • Dede, M., Ekici, C., Directional Bertrand curves, Gazi Univ. J. Sci., 31(1) (2018), 202–211.
  • Dede, M., Aslan, M. Ç., Ekici, C., On a variational problem due to the B-Darboux frame in Euclidean 3-space, Math. Methods Appl. Sci., 44(17) (2021), 12630–12639. https://doi.org/10.1002/mma.7567
  • Goldstein, H., Poole, C. P., Safko, J. L., Classical Mechanics, Vol. 2, Reading, MA: Addison-Wesley, 1950.
  • Görgülü, A., A generalization of the Bertrand curves as general inclined curves in $E^n$, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 35(01.02) (1986), 54–60. https://doi.org/10.1501/Commua1 0000000254
  • Gürbüz, N. E., The evolution of an electric field with respect to the type-1 PAF and the PAFORS frames in $R^3_1$, Optik, 250(1) (2022), 168285. https://doi.org/10.1016/j.ijleo.2021.168285
  • Izumiya, S., Takeuchi, N., Generic properties of helices and Bertrand curves, J. Geom., 74 (2002), 97–109. https://doi.org/10.1007/PL00012543
  • İlarslan, K., Nesovic, E., Some characterizations of osculating curves in the Euclidean spaces, Demonstr. Math., 41(4) (2008), 931–939. https://doi.org/10.1515/dema-2008-0421
  • Kazaz, M., Uğurlu, M. M., Önder, M., Oral, S., Bertrand partner D-curves in the Euclidean 3-space $E^3$, Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, 16(1) (2016), 76–83. https://doi.org/10.5578/fmbd.25270
  • Özen, K. E., Tosun, M., A new moving frame for trajectories with non-vanishing angular momentum, J. Math. Sci. Model., 4(1) (2021), 7–18. https://doi.org/10.33187/jmsm.869698
  • Özen, K. E., Tosun, M., Trajectories generated by special Smarandache curves according to Positional Adapted Frame, Karamanoğlu Mehmetbey University Journal of Engineering and Natural Sciences, 3(1) (2021), 15–23.
  • Papaioannou, S. G., Kiritsis, D., An application of Bertrand curves and surfaces to CADCAM, Computer-Aided Design, 17(8) (1985), 348–352. https://doi.org/10.1016/0010-4485(85)90025-9
  • Shifrin T., Differential Geometry: A First Course in Curves and Surfaces, University of Georgia, Preliminary Version, 2008.
  • Solouma, E. M., Characterization of Smarandache trajectory curves of constant mass point particles as they move along the trajectory curve via PAF, Bulletin of Mathematical Analysis and Applications, 13(4) (2021), 14–30. https://doi.org/10.54671/bmaa-2021-4-2
  • Whittemore, J. K., Bertrand curves and helices, Duke Math. J., 6(1) (1940), 235–245. https://doi.org/10.1215/S0012-7094-40-00618-4
  • Yerlikaya, F., Karaahmetoğlu, S., Aydemir, İ., On the Bertrand B-pair curve in 3-dimensional Euclidean space, Journal of Science and Arts, 3(36) (2016), 215–224.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Zehra İşbilir 0000-0001-5414-5887

Kahraman Esen Özen 0000-0002-3299-6709

Murat Tosun 0000-0002-4888-1412

Yayımlanma Tarihi 30 Mart 2023
Gönderilme Tarihi 27 Mart 2022
Kabul Tarihi 29 Eylül 2022
Yayımlandığı Sayı Yıl 2023 Cilt: 72 Sayı: 1

Kaynak Göster

APA İşbilir, Z., Özen, K. E., & Tosun, M. (2023). Bertrand partner P-trajectories in the Euclidean 3-space $E^3$. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(1), 216-228. https://doi.org/10.31801/cfsuasmas.1094170
AMA İşbilir Z, Özen KE, Tosun M. Bertrand partner P-trajectories in the Euclidean 3-space $E^3$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Mart 2023;72(1):216-228. doi:10.31801/cfsuasmas.1094170
Chicago İşbilir, Zehra, Kahraman Esen Özen, ve Murat Tosun. “Bertrand Partner P-Trajectories in the Euclidean 3-Space $E^3$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, sy. 1 (Mart 2023): 216-28. https://doi.org/10.31801/cfsuasmas.1094170.
EndNote İşbilir Z, Özen KE, Tosun M (01 Mart 2023) Bertrand partner P-trajectories in the Euclidean 3-space $E^3$. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 1 216–228.
IEEE Z. İşbilir, K. E. Özen, ve M. Tosun, “Bertrand partner P-trajectories in the Euclidean 3-space $E^3$”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 72, sy. 1, ss. 216–228, 2023, doi: 10.31801/cfsuasmas.1094170.
ISNAD İşbilir, Zehra vd. “Bertrand Partner P-Trajectories in the Euclidean 3-Space $E^3$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/1 (Mart 2023), 216-228. https://doi.org/10.31801/cfsuasmas.1094170.
JAMA İşbilir Z, Özen KE, Tosun M. Bertrand partner P-trajectories in the Euclidean 3-space $E^3$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:216–228.
MLA İşbilir, Zehra vd. “Bertrand Partner P-Trajectories in the Euclidean 3-Space $E^3$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 72, sy. 1, 2023, ss. 216-28, doi:10.31801/cfsuasmas.1094170.
Vancouver İşbilir Z, Özen KE, Tosun M. Bertrand partner P-trajectories in the Euclidean 3-space $E^3$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(1):216-28.

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

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