New results for general helix in Euclidean 3-space. (English) Zbl 1469.53008
Tosun, Murat (ed.) et al., 6th international Eurasian conference on mathematical sciences and applications, IECMSA-2017, Budapest, Hungary, August 15–18 August, 2017. Melville, NY: American Institute of Physics (AIP). AIP Conf. Proc. 1926, Article 020017, 6 p. (2018).
Summary: Finding parametric equation of a space curve is not easy task when its curvature functions are given. It is well known that this problem is known as fundamental theorem of a space curve. If the curvature functions are functions of arc-length, the solution of this problem is usually impossible. In this study, we discuss the answer of the problem when the curve is a general helix in Euclidean 3-space. By using slope axis of general helix, we get parametric equations of a general helix. Also, we give some examples and their figures.
For the entire collection see [Zbl 1437.00037].
For the entire collection see [Zbl 1437.00037].
MSC:
| 53A04 | Curves in Euclidean and related spaces |
References:
| [1] | Ali, A. T., Nonlinear Anal., 73, 4, 1118-1126 (2010) · Zbl 1209.53005 · doi:10.1016/j.na.2010.04.051 |
| [2] | Arroyo, J.; Barros, M.; Garay, J. O., Bull. Austral. Math. Soc., 56, 1, 37-49 (1997) · Zbl 0886.53039 · doi:10.1017/S0004972700030719 |
| [3] | Barros, M.; Ferrández, A., J. Math. Biol., 69, 1801-1813 (2014) · Zbl 1353.92068 · doi:10.1007/s00285-013-0752-9 |
| [4] | Barros, M.; Ferrández, A., J. Math. Phys., 50, 10, 20 (2009) · Zbl 1283.53003 · doi:10.1063/1.3236683 |
| [5] | Barros, M.; Ferrández, A.; Lucas, P.; Mero��o, M. A., Rocky Mountain J. Math., 31, 2, 373-388 (2001) · Zbl 0985.53009 · doi:10.1216/rmjm/1020171565 |
| [6] | Barros, M., Proc. Amer. Math. Soc., 125, 5, 1503-1509 (1997) · Zbl 0876.53035 · doi:10.1090/S0002-9939-97-03692-7 |
| [7] | Camci, Ç.; İlarslan, K.; Kula, L.; Hacisalihoglu, H. H., Chaos, Solitons and Fractals, 40, 1-7 (2007) |
| [8] | Camci, Ç., İlarslan, K. and Ucum, A., General Helices with lightlike slope axis, to appear in Filomat, 2016. · Zbl 1342.53020 |
| [9] | Çiftçi, Ü., J. Geom. Phys., 59, 12, 1597-1603 (2009) · Zbl 1177.53009 · doi:10.1016/j.geomphys.2009.07.016 |
| [10] | Ekmekci, N.; İlarslan, K., Bol. Soc. Mat. Mexicana, 9, 2, 279-286 (2003) · Zbl 1076.53014 |
| [11] | Ferrández, A.; Giménez, A.; Lucas, P., J. Phys. A, 35, 39, 8243-8251 (2002) · Zbl 1052.53028 · doi:10.1088/0305-4470/35/39/308 |
| [12] | Ferrández, A.; Giménez, A.; Lucas, P., Internat. J. Modern Phys. A, 16, 30, 4845-4863 (2001) · Zbl 1003.53052 · doi:10.1142/S0217751X01005821 |
| [13] | Ferrández, A.; Giménez, A.; Lucas, P., Null generalized helices and the Betchov-Da Rios equation in Lorentz-Minkowski spaces, Publ. R. Soc. Mat. Esp., 215-221 (2004) · Zbl 1068.53020 |
| [14] | Forterre, Y.; Dumais, J., J., Science, 333, 6050, 1715-1716 · doi:10.1126/science.1210734 |
| [15] | Hayden, H. A., Proc. London Math. Soc., S2-32, 1, 337-45 · JFM 57.0930.04 · doi:10.1112/plms/s2-32.1.337 |
| [16] | İlarslan, K.; Boyacıoğlu, Ö., Chaos Solitons Fractals, 38, 5, 1383-1389 (2008) · Zbl 1154.53304 · doi:10.1016/j.chaos.2008.04.003 |
| [17] | Kuhnel, W., Differential geometry: curves-surfaces-manifolds (1999), Wiesbaden: Wiesbaden, Braunchweig · Zbl 0931.53001 |
| [18] | Lancret, M. A., Mémoire sur les courbes à double courbure, Mémoires présentés à l’Institut1, 416-454 (1806) |
| [19] | Nesovic, E.; Öztürk, U.; Koç Öztürk, E. B., J. Math. Anal. Appl., 439, 690-700 (2016) · Zbl 1337.53031 |
| [20] | O’Neill, B., Pure and Applied Mathematics, Semi-Riemannian geometry. With applications to relativity (1983), Academic Press, Inc.: Academic Press, Inc., New York · Zbl 0531.53051 |
| [21] | Özdamar, E.; Hacisalihoglu, H. H., Comm. Fac Sci Univ. Ankara, Ser A1, 24, 15-23 (1975) · Zbl 0361.53006 |
| [22] | Öztürk, U.; Nesovic, E., Kuwait J. Sci., 43, 2, 161-179 (2016) |
| [23] | Sy, S., General helices and other topics in the differentiak geometry of curves, a report : submitted in partial fulfillment of the requirements for the degree of master of science in mathematics, Michigan Tech. University (2001) |
| [24] | Uçum, A.; Çamci, Ç.; İlarslan, K., Advances in Applied Clifford Algebras, 26, 2, 793-807 (2016) · Zbl 1342.53020 · doi:10.1007/s00006-015-0610-5 |
| [25] | Yang, X., Comput Aided Geometric Design, 20, 303-17 (2003) · Zbl 1069.65540 · doi:10.1016/S0167-8396(03)00074-8 |
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