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Journal articles on the topic 'Frenet'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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1

Önder, Mehmet, and Hasan Hüseyin Uğurlu. "Spacelike Regle Yüzeylerin Frenet Çatıları ve Frenet İnvaryantları." Deu Muhendislik Fakultesi Fen ve Muhendislik 19, no. 57 (January 1, 2017): 712–22. http://dx.doi.org/10.21205/deufmd.2017195764.

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2

Arreaga, G., R. Capovilla, and J. Guven. "Frenet–Serret dynamics." Classical and Quantum Gravity 18, no. 23 (November 22, 2001): 5065–83. http://dx.doi.org/10.1088/0264-9381/18/23/304.

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3

Encheva, Radostina P., and Georgi H. Georgiev. "Similar Frenet Curves." Results in Mathematics 55, no. 3-4 (August 7, 2009): 359–72. http://dx.doi.org/10.1007/s00025-009-0407-8.

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4

ATEŞ, Fatma, Seher KAYA, Yusuf YAYLI, and F. Nejat EKMEKCİ. "Generalized Similar Frenet Curves." Mathematical Sciences and Applications E-Notes 5, no. 2 (October 30, 2017): 26–36. http://dx.doi.org/10.36753/mathenot.421731.

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5

Capovilla, R., J. Guven, and E. Rojas. "Hamiltonian Frenet–Serret dynamics." Classical and Quantum Gravity 19, no. 8 (April 2, 2002): 2277–90. http://dx.doi.org/10.1088/0264-9381/19/8/315.

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6

Capovilla, R., J. Guven, and E. Rojas. "Null Frenet-Serret dynamics." General Relativity and Gravitation 38, no. 4 (February 25, 2006): 689–98. http://dx.doi.org/10.1007/s10714-006-0258-5.

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7

Bektaş, Özcan, and Salim Yüce. "Serret-Frenet formulas for octonionic curves." Boletim da Sociedade Paranaense de Matemática 38, no. 3 (February 18, 2019): 47–62. http://dx.doi.org/10.5269/bspm.v38i3.34780.

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In this paper, we dene spatial octonionic curves (SOC) in R7 and octonionic curves (OC) in R8 by using octonions. Firstly, we determine Serret-Frenet equations, and curvatures of the SROC in R7. Then, Serret-Frenet equations for the OC in R8 are calculated with the help of Serret-Frenet equations of SOC in R7.

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8

El-Ahmady, A. E., and A. T. M-Zidan. "On the Deformation Retractions of Frenet Curves in Minkowski 4 - Space." Modern Applied Science 14, no. 9 (August 28, 2020): 55. http://dx.doi.org/10.5539/mas.v14n9p55.

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In this paper, the position vector equation of   the Frenet curves with constant curvatures in Minkowski 4 -space has been presented. New types for retractions and deformation retracts of Frenet curves in  are deduced. The relations between the Frenet apparatus of the Frenet curves before and after the deformation retracts are obtained.

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9

CAVASI, ABEL. "The recurrence theorem of Frenet formulae." Creative Mathematics and Informatics 23, no. 2 (2014): 175–82. http://dx.doi.org/10.37193/cmi.2014.02.15.

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In this paper we generalize Frenet trihedron and we provide some other classes of trihedrons, called Frenet trihedrons of order n, n ≥ 1. Moreover we prove that those trihedrons can be defined recurrently and we emphasize their role in the study of the generalized helices of order n. As practical applications we present the influence of the recurrence theorem in some interdisciplinary domains like physics, chemistry and biology.

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10

Avanzini, Giulio. "Frenet-Based Algorithm for Trajectory Prediction." Journal of Guidance, Control, and Dynamics 27, no. 1 (January 2004): 127–35. http://dx.doi.org/10.2514/1.9338.

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11

Viana, Thiago Mariano, and Fernando Pereira Souza. "CURVAS REGULARES E EQUAÇÕES DE FRENET." Colloquium Exactarum 4, Especial (October 25, 2013): 01–09. http://dx.doi.org/10.5747/ce.2013.v05.nesp.000046.

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12

Ali, Md Showkat, and Md Abu Hanif Sarkar. "Serret-Frenet Equations in Minkowski Space." Dhaka University Journal of Science 61, no. 1 (May 27, 2013): 87–92. http://dx.doi.org/10.3329/dujs.v61i1.15102.

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In this paper we established the Serret-Frenet equations in Minkowski space. These equations originally formulated in Euclidean space in R3, constitute a beautiful set of vector differential equations which contains all intrinsic properties of parameterized curve. From the local theory of curves in R3 states that a curve lies in a plane if and only if its torsion vanishes, which gives us clear geometrical insight in the notion of torsion. This theorem has two counterparts in Minkowski space that has been focused. Dhaka Univ. J. Sci. 61(1): 87-92, 2013 (January) DOI: http://dx.doi.org/10.3329/dujs.v61i1.15102

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13

DESHMUKH, Sharief, İbrahim AL-DAYEL, and Kazım İLARSLAN. "Frenet Curves in Euclidean 4-Space." International Electronic Journal of Geometry 10, no. 2 (October 29, 2017): 56–66. http://dx.doi.org/10.36890/iejg.545050.

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14

Wagner, Michael G., and Bahram Ravani. "Curves with rational Frenet-Serret motion." Computer Aided Geometric Design 15, no. 1 (December 1997): 79–101. http://dx.doi.org/10.1016/s0167-8396(97)81786-4.

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15

UNDERWOOD, MICHAEL S., and KARL-PETER MARZLIN. "FERMI–FRENET COORDINATES FOR SPACELIKE CURVES." International Journal of Modern Physics A 25, no. 06 (March 10, 2010): 1147–54. http://dx.doi.org/10.1142/s0217751x10047841.

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We generalize Fermi coordinates, which correspond to an adapted set of coordinates describing the vicinity of an observer's worldline, to the worldsheet of an arbitrary spatial curve in a static spacetime. The spatial coordinate axes are fixed using a covariant Frenet triad so that the metric can be expressed using the curvature and torsion of the spatial curve. As an application of Fermi–Frenet coordinates, we show that they allow covariant inertial forces to be expressed in a simple and physically intuitive way.

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16

Tjahjana, R. H., and R. H. S. Utomo. "Multi agent through serret-frenet system." Journal of Physics: Conference Series 1321 (October 2019): 022071. http://dx.doi.org/10.1088/1742-6596/1321/2/022071.

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17

Iyer, B. R., and C. V. Vishveshwara. "Frenet-Serret description of gyroscopic precession." Physical Review D 48, no. 12 (December 15, 1993): 5706–20. http://dx.doi.org/10.1103/physrevd.48.5706.

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18

Yılmaz, Süha, and Yasin Unluturk. "On spherical indicatrices of curves in Galilean 4-space G₄." Journal of the Indonesian Mathematical Society 25, no. 2 (July 15, 2019): 154–70. http://dx.doi.org/10.22342/jims.25.2.473.154-170.

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In this study, we indroduce spherical indicatrices of curves in four dimensional Galilean space. Moreover, we characterize these curves in terms of Frenet-Serret vector fields in four dimensional Galilean space. Frenet-Serret apparatus of these curves are obtained in terms of base curve's Frenet invariants. Additionally, some theorems are given regarding characterizations of spherical indicatrices of curves in four dimensional Galilean space.

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19

Yormaz, Cansel, Simge Simsek, and Serife Naz Elmas. "Quaternionic Serret-Frenet Frames for Fuzzy Split Quaternion Numbers." Advances in Fuzzy Systems 2018 (2018): 1–6. http://dx.doi.org/10.1155/2018/7215049.

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We build the concept of fuzzy split quaternion numbers of a natural extension of fuzzy real numbers in this study. Then, we give some differential geometric properties of this fuzzy quaternion. Moreover, we construct the Frenet frame for fuzzy split quaternions. We investigate Serret-Frenet derivation formulas by using fuzzy quaternion numbers.

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20

El-Ahmady, A. E., Malak E. Raslan, and A. T. M-Zidan. "On Null Curves in Minkowski 3-Space and Its Fractal Folding." Modern Applied Science 14, no. 4 (March 27, 2020): 90. http://dx.doi.org/10.5539/mas.v14n4p90.

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In this paper, a form for Frenet equations of all null curves in Minkowski 3-space has been presented. New types of foldings of curves are obtained. The connection between folding, deformation and Frenet equations of curves are also deduced.

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21

Abadoğlu, E., and H. Gūmral. "Bi-Hamiltonian structure in Frenet–Serret frame." Physica D: Nonlinear Phenomena 238, no. 5 (March 2009): 526–30. http://dx.doi.org/10.1016/j.physd.2008.11.013.

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22

Bini, Donato, Andrea Geralico, and Robert T. Jantzen. "Frenet–Serret formalism for null world lines." Classical and Quantum Gravity 23, no. 11 (May 12, 2006): 3963–81. http://dx.doi.org/10.1088/0264-9381/23/11/018.

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23

Gözütok, Uğur, Hüsnü Çoban, and Yasemin Sağıroğlu. "Frenet frame with respect to conformable derivative." Filomat 33, no. 6 (2019): 1541–50. http://dx.doi.org/10.2298/fil1906541g.

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Conformable fractional derivative is introduced by the authors Khalil at al in 2014. In this study, we investigate the frenet frame with respect to conformable fractional derivative. Curvature and torsion of a conformable curve are defined and the geometric interpretation of these two functions is studied. Also, fundamental theorem of curves is expressed for the conformable curves and an example of the curve corresponding to a fractional differential equation is given.

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24

Casanova, Gaston. "Algèbre de Clifford et formules de frenet." Advances in Applied Clifford Algebras 10, no. 1 (June 2000): 45–47. http://dx.doi.org/10.1007/bf03042008.

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25

Han, Chang Yong, and Song-Hwa Kwon. "Cubic helical splines with Frenet-frame continuity." Computer Aided Geometric Design 28, no. 7 (October 2011): 395–406. http://dx.doi.org/10.1016/j.cagd.2011.08.003.

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26

Kahveci̇, Derya, and Yusuf Yayli. "Persistent rigid-body motions on slant helices." International Journal of Geometric Methods in Modern Physics 16, no. 12 (November 29, 2019): 1950193. http://dx.doi.org/10.1142/s0219887819501937.

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This paper reviews the persistent rigid-body motions and examines the geometric conditions of the persistence of some special frame motions on a slant helix. Unlike the Frenet–Serret motion on general helices, the Frenet–Serret motion on slant helices can be persistent. Moreover, even the adapted frame motion on slant helices can be persistent. This paper begins by explaining one-dimensional rigid-body motions and persistent motions. Then, it continues to present persistent frame motions in terms of their instantaneous twists and axode surfaces. Accordingly, the persistence of any frame motions attached to a curve can be characterized by the pitch of an instantaneous twist. This work investigates different frame motions that are persistent, namely frame motions whose instantaneous twist has a constant pitch. In particular, by expressing the connection between the pitch of Frenet–Serret motion and the pitch of adapted frame motion, it demonstrates that both the Frenet–Serret motion and the adapted frame motion are persistent on slant helices.

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27

Kılıçoğlu, Şeyda, and Süleyman Şenyurt. "On the Involute of the Cubic Bezier Curve by Using Matrix Representation in E3." European Journal of Pure and Applied Mathematics 13, no. 2 (April 29, 2020): 216–26. http://dx.doi.org/10.29020/nybg.ejpam.v13i2.3648.

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In this study we have examined, involute of the cubic Bezier curve based on the control points with matrix form in E3. Frenet vector fields and also curvatures of involute of the cubic Bezier curve are examined based on the Frenet apparatus of the first cubic Bezier curve in E3.

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28

Iyigün, Esen. "Constant curvature ratios in L6." Filomat 30, no. 3 (2016): 785–89. http://dx.doi.org/10.2298/fil1603785i.

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In this paper, we find a relation between Frenet formulas and harmonic curvatures, and also a relation between Frenet formulas and e-curvature functions of a curve of osculating order 6 in 6 dimensional Lorentzian space L6. Moreover, we give a relation between harmonic curvatures and ccr-curves of a curve in L6.

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29

Körpınar, Talat, and Ridvan Cem Demirkol. "A new construction on the energy of space curves in unit vector fields in Minkowski space E₂⁴." Boletim da Sociedade Paranaense de Matemática 39, no. 2 (January 1, 2021): 105–20. http://dx.doi.org/10.5269/bspm.39288.

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In this paper, we firstly introduce kinematics properties of a moving particle lying in Minkowski space E₂⁴. We assume that particles corresponds to different type of space curves such that they are characterized by Frenet frame equations. Guided by these, we present geometrical understanding of an energy and pseudo angle on the particle in each Frenet vector fields depending on the particle corresponds to a spacelike, timelike or lightlike curve in E₂⁴. Then we also determine the bending elastic energy functional for the same particle in E₂⁴ by assuming the particle has a bending feature of elastica. Finally, we prove that bending energy formula can be represented by the energy on the particle in each Frenet vector field.

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30

Tunçer, Yılmaz. "Vectorial moments of curves in Euclidean 3-space." International Journal of Geometric Methods in Modern Physics 14, no. 02 (January 18, 2017): 1750020. http://dx.doi.org/10.1142/s0219887817500207.

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In this study, we introduced the vectorial moments as a new curves as [Formula: see text]-dual curve, where [Formula: see text], constructed by the Frenet vectors of a regular curve in Euclidean 3-space and we gave the Frenet apparatus of [Formula: see text]-dual curves and also we applied to helices and curve pairs of constant breadth.

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31

Wang, J., and J. Xiao. "Exact Finite Element Formulation of Frenet Formula of Curve in Geospatial Database." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-4 (April 23, 2014): 291–95. http://dx.doi.org/10.5194/isprsarchives-xl-4-291-2014.

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Directly using the difference form of Frenet formula will cause the three basic vectors losing their orthogonal features rapidly. As the analytic form is exact for infinite short length region, for finite length segregation, the omitted items should be retrieved to get high precision. Based on the unit orthogonal transformation in geometrical field theory, the Frenet formula is reformed for finite length region. Then, for given triple at the initial end of curve, using the curve parameters of curvature and torsion, the exact finite element formulation of Frenet formula is obtained to get the triples at any length position until the end point of curve. This method can be used as a high-precision technology for the measure, store, and retrieve of complicated curve.

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32

Erkan, Esra, and Salim Yüce. "Serret-Frenet Frame and Curvatures of Bézier Curves." Mathematics 6, no. 12 (December 12, 2018): 321. http://dx.doi.org/10.3390/math6120321.

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The aim of this study is to view the role of Bézier curves in both the Euclidean plane E 2 and Euclidean space E 3 with the help of the fundamental algorithm which is commonly used in Computer Science and Applied Mathematics and without this algorithm. The Serret-Frenet elements of non-unit speed curves in the Euclidean plane E 2 and Euclidean space E 3 are given by Gray et al. in 2016. We used these formulas to find Serret-Frenet elements of planar Bézier curve at the end points and for every parameter t. Moreover, we reconstruct these elements for a planar Bézier curve, which is defined by the help of the algorithm based on intermediate points. Finally, in the literature, the spatial Bézier curve only mentioned at the end points, so we improve these elements for all parameters t. Additionally, we calculate these elements for all parameters t using algorithm above mentioned for spatial Bézier curve.

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33

Amirov, Rauf, and Tuğba Mert. "Frenet Diferansiyel Denklem Sisteminin Çözümleri İçin İntegral Gösterimleri." Cumhuriyet Science Journal 35, no. 2 (August 4, 2014): 11. http://dx.doi.org/10.17776/csj.68151.

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34

Zhou, Xiaozhou, and Keqin Zhu. "A note on natural coordinates and frenet frames." Tsinghua Science and Technology 12, no. 3 (June 2007): 252–55. http://dx.doi.org/10.1016/s1007-0214(07)70037-8.

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35

Bakırcioğlu, M., U. Grenander, N. Khaneja and, and M. I. Miller. "Curve matching on brain surfaces using frenet distances." Human Brain Mapping 6, no. 5-6 (1998): 329–33. http://dx.doi.org/10.1002/(sici)1097-0193(1998)6:5/6<329::aid-hbm1>3.0.co;2-x.

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36

Zeki Okuyucu, Osman, Önder Gökmen Yıldız, and Murat Tosun. "Spinor Frenet Equations in Three Dimensional Lie Groups." Advances in Applied Clifford Algebras 26, no. 4 (March 12, 2016): 1341–48. http://dx.doi.org/10.1007/s00006-016-0651-4.

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37

Kimura, Makoto, and Miguel Ortega. "Congruence classes of Frenet curves in complex quadrics." Journal of Geometry 83, no. 1-2 (December 2005): 121–36. http://dx.doi.org/10.1007/s00022-005-0001-5.

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38

Önder, Mehmet, and H. Hüseyin Uğurlu. "Frenet frames and invariants of timelike ruled surfaces." Ain Shams Engineering Journal 4, no. 3 (September 2013): 507–13. http://dx.doi.org/10.1016/j.asej.2012.10.003.

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39

Cabrer, Leonardo Manuel, and Daniele Mundici. "Severi–Bouligand tangents, Frenet frames and Riesz spaces." Advances in Applied Mathematics 64 (March 2015): 1–20. http://dx.doi.org/10.1016/j.aam.2014.11.004.

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40

Goodman, T. N. T. "Constructing piecewise rational curves with Frenet frame continuity." Computer Aided Geometric Design 7, no. 1-4 (June 1990): 15–31. http://dx.doi.org/10.1016/0167-8396(90)90018-m.

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41

Güven, Ìlkay Arslan, Semra Kaya Nurkan, and Ìpek Agaoglu Tor. "Spherical Images of W-Direction Curves in Euclidean 3-Space." Journal of Mathematics Research 12, no. 3 (May 6, 2020): 39. http://dx.doi.org/10.5539/jmr.v12n3p39.

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In this paper, we study the spherical indicatrices of W-direction curves in three dimensional Euclidean space which were defined by using the unit Darboux vector field W of a Frenet curve. We obtain the Frenet apparatus of these spherical indicatrices and the characterizations of being general helix and slant helix. Moreover we give some properties between the spherical indicatrices and their associated curves.

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42

Yajima, Takahiro, Shunya Oiwa, and Kazuhito Yamasaki. "Geometry of curves with fractional-order tangent vector and Frenet-Serret formulas." Fractional Calculus and Applied Analysis 21, no. 6 (December 19, 2018): 1493–505. http://dx.doi.org/10.1515/fca-2018-0078.

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Abstract This paper discusses a construction of fractional differential geometry of curves (curvature of curve and Frenet-Serret formulas). A tangent vector of plane curve is defined by the Caputo fractional derivative. Under a simplification for the fractional derivative of composite function, a fractional expression of Frenet frame of curve is obtained. Then, the Frenet-Serret formulas and the curvature are derived for the fractional ordered frame. The different property from the ordinary theory of curve is given by the explicit expression of arclength in the fractional-order curvature. The arclength part of the curvature takes a large value around an initial time and converges to zero for a long period of time. This trend of curvature may reflect the memory effect of fractional derivative which is progressively weaken for a long period of time. Indeed, for a circle and a parabola, the curvature decreases over time. These results suggest that the basic property of fractional derivative is included in the fractional-order curvature appropriately.

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43

Uçar, Ayşenur, Fatma Karakuş, and Yusuf Yaylı. "Generalized Fermi–Walker derivative and non-rotating frame." International Journal of Geometric Methods in Modern Physics 14, no. 09 (August 2, 2017): 1750131. http://dx.doi.org/10.1142/s0219887817501316.

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In this paper, generalized Fermi–Walker derivative, generalized Fermi–Walker parallelism and generalized non-rotating frame concepts are given for Frenet frame, Darboux frame and Bishop frame for any curve in Euclidean space. Being generalized, non-rotating frame conditions are analyzed for each frames along the curve. Then we show that Frenet and Darboux frames are generalized non-rotating frames along all curves and also Bishop frame is generalized non-rotating frame along planar curves in Euclidean space.

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44

Chen, J. T., J. W. Lee, S. K. Kao, and Y. T. Chou. "Construction of a curve by using the state equation of Frenet formula." Journal of Mechanics 37 (2021): 454–65. http://dx.doi.org/10.1093/jom/ufab014.

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Abstract In this paper, the available formulae for the curvature of plane curve are reviewed not only for the time-like but also for the space-like parameter curve. Two ways to describe the curve are proposed. One is the straight way to obtain the Frenet formula according to the given curve of parameter form. The other is that we can construct the curve by solving the state equation of Frenet formula subject to the initial position, the initial tangent, normal and binormal vectors, and the given radius of curvature and torsion constant. The remainder theorem of the matrix and the Cayley–Hamilton theorem are both employed to solve the Frenet equation. We review the available formulae of the radius of curvature and examine their equivalence. Through the Frenet formula, the relation among different expressions for the radius of curvature formulae can be linked. Therefore, we can integrate the formulae in the engineering mathematics, calculus, mechanics of materials and dynamics. Besides, biproduct of two new and simpler formulae and the available four formulae in the textbook of the radius of curvature yield the same radius of curvature for the plane curve. Linkage of centrifugal force and radius of curvature is also addressed. A demonstrative example of the cycloid is given. Finally, we use the two new formulae to obtain the radius of curvature for four curves, namely a circle. The equivalence is also proved. Animation for 2D and 3D curves is also provided by using the Mathematica software to demonstrate the validity of the present approach.

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45

Durić, Zoran, Azriel Rosenfeld, and Larry S. Davis. "Egomotion analysis based on the Frenet-Serret motion model." International Journal of Computer Vision 15, no. 1-2 (June 1995): 105–22. http://dx.doi.org/10.1007/bf01450851.

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46

Choi, Jin Ho, and Young Ho Kim. "Associated curves of a Frenet curve and their applications." Applied Mathematics and Computation 218, no. 18 (May 2012): 9116–24. http://dx.doi.org/10.1016/j.amc.2012.02.064.

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47

Choi, Jin Ho, Young Ho Kim, and Ahmad T. Ali. "Some associated curves of Frenet non-lightlike curves inE13." Journal of Mathematical Analysis and Applications 394, no. 2 (October 2012): 712–23. http://dx.doi.org/10.1016/j.jmaa.2012.04.063.

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48

Kim, Kwang-Rae, Peter T. Kim, Ja-Yong Koo, and Michael R. Pierrynowski. "Frenet-Serret and the Estimation of Curvature and Torsion." IEEE Journal of Selected Topics in Signal Processing 7, no. 4 (August 2013): 646–54. http://dx.doi.org/10.1109/jstsp.2012.2232280.

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49

Yang, Kichoon. "Frenet formulae for holomorphic curves in the two quadric." Bulletin of the Australian Mathematical Society 33, no. 2 (April 1986): 195–206. http://dx.doi.org/10.1017/s0004972700003063.

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50

Abd-Ellah, H. N. "Motion of Bishop Frenet Offsets of Ruled Surfaces inE3." Journal of Applied Mathematics 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/218956.

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The main goal of this paper is to study the motion of two associated ruled surfaces in Euclidean 3-spaceE3. In particular, the motion of Bishop Frenet offsets of ruled surfaces is investigated. Additionally, the characteristic properties for such ruled surfaces are given. Finally, an application is presented and plotted using computer aided geometric design.

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