×

A different view on dynamics of space curves geometry. (English) Zbl 1486.53008

Summary: In this study, we define the \(X\)-torque curves, \(X-\) equilibrium curves, \(X\)-moment conservative curves, \(X-\) gyroscopic curves as new curves derived from a regular space curve by using the Frenet vectors of a space curve and its position vector, where \(X\in \left\{ T(s), N(s), B(s) \right\}\) and we examine these curves and we give their properties.

MSC:

53A04 Curves in Euclidean and related spaces
53A05 Surfaces in Euclidean and related spaces
53C40 Global submanifolds
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Serway, R.A., Jewett, J.W.: Physics for Scientists and Engineers, (6th Ed. Brooks Cole, ISBN 0-534-40842-7) (2003)
[2] Urone, P., Hinrich, R.: College Physics (Open Licensed E-book, Openstax, LibreTexts, https://phys.libretexts.org/@go/page/1558)
[3] Kibele, A.; Granacher, U.; Muehlbauer, T.; Behm, DG, Stable, unstable, and metastable states of equilibrium: definitions and applications to human movement, J. Sports Sci. Med., 14, 885-887 (2015)
[4] Bottema, O.; Roth, B., Theoretical Kinematics (1979), Amsterdam: North-Holland, Amsterdam · Zbl 0405.70001
[5] Tuncer, Y., Vectorial moments of curves in Euclidean 3-space, Int. J. Geom. Methods Modern Phys., 14, 2, 1750020 (2017) · Zbl 1357.53010 · doi:10.1142/S0219887817500207
[6] Chen, BY, When does the position vector of a space curve always lie in its rectifying plane?, Am. Math. Monthly, 110, 147-152 (2003) · Zbl 1035.53003 · doi:10.1080/00029890.2003.11919949
[7] Camcı, Ç.; Kula, L.; İlarslan, K., Characterizations of the position vector of a surface curve in Euclidean 3-space, An Şt Ovidius Constanta, 19, 3, 59-70 (2011) · Zbl 1274.53001
[8] Barros, M., General helices and a theorem of Lancret, Proc. Am. Math. Monthly, 125, 1503-1509 (1997) · Zbl 0876.53035 · doi:10.1090/S0002-9939-97-03692-7
[9] Lancret, MA, Memoire sur les courbes a double courbure, Memoires Present es a l’Institut, 1, 416-454 (1802)
[10] Struik, DJ, Lectures on Classical Differential Geometry (1988), New-York: Dover, New-York · Zbl 0697.53002
[11] Yavuz, A.; Yaylı, Y., Ruled surfaces with constant slope ruling according to Darboux frame in Minkowski space, Int. J. Anal. Appl., 18, 6, 900-919 (2020)
[12] Şenyurt,, S.; cSardağ, H.; Çakır, O., On vectorial moment of the Darboux vector, Konuralp J. Math., 8, 2, 144-151 (2020)
[13] Şenyurt, S.; Çalışkan, A., Curves and ruled surfaces according to alternative frame in dual space, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat, 69, 1, 684-698 (2020) · Zbl 1495.53013
[14] Ateş, F.; Gök, İ.; Ekmekci, FN; Yaylı, Y., Characterizations of inclined curves according to parallel transport frame in \(E^4\) and Bishop frame in \(E^3\), Konuralp J. Math., 7, 1, 16-24 (2019) · Zbl 1438.53003
[15] Monterde, J., Curves with constant curvature ratios, Bol. Soc. Mat. Mexicana, 3, 13-1, 177-186 (2007) · Zbl 1177.53015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.