Spherical indicatrix
Webdifferential equations verified for each one of spherical indicatrix in Euclidean 3-space. Beyhan uzunoğlu, Ismail GÖk & Yusuf Yayli (2013), investigated a curve whose spherical images (the tangent indicatrice and binormal indicatrix) are slant helices and called it a slant-slant helix and have given some characterizations. We obtain WebSPHERICAL INDICATRIX. The spherical indicatrix of curvature of a 3D curve is the trajectory (included in the sphere with center O and radius 1) of the point P such that where is the …
Spherical indicatrix
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WebThe curvature and torsion of the tangent indicatrix. Let $\alpha$ be a unit speed curve. Its tangent indicatrix $\sigma$ is defined by $\sigma (t)=T (t)$. Find torsion and curvature of $\sigma$ with respect to the torsion and curvature of $\alpha$. There is an answer on my book. But I don't understand (*) part. WebIn this paper, we give some characterizations of constant slope surfaces and Bertrand curves in Euclidean 3-space. We find parametrization of constant slope surfaces for spherical images of tangent i
WebSep 12, 2009 · The theory of spherical indicatrix of space curves in Riemannian geometry also has been studied by [2], [7] and [12] while the study of spherical indicatrix of curves … WebWe investigate a new representation of binormal spherical indicatrices of magnetic curves. Thus, we study B b -magnetic curves terms of inextensible flows. Furthermore, we give …
WebAug 15, 2016 · Spherical indicatrices of isotropic curves in Definition 3.1 Let be a regular isotropic curve in . If we translate the first vector field of E. Cartan frame to the center O of the unit isotropic sphere , then we obtain spherical image . This curve is called spherical image or indicatrix of the isotropic curve . Theorem 3.1 http://fs.unm.edu/IJMC/The_Natural_Lift_Curve_of_the_Spherical_Indicatrix_of_a_Curve_According_to_Bishop_Frame_in_Euclidean_3-Space.pdf
WebNov 26, 2024 · The semi-axes of this optical indicatrix are directly proportional to the principal refractive indices. Optically isotropic materials (e.g. cubic crystals) have one …
WebIn this work, the directional spherical indicatrices of a timelike space curve using tangent, quasi-normal and quasi-binormal vectors with q-frame are introduced. Then we work on the condition, that a timelike space curve to be slant helix, by using the geodesic curvature of the directional normal spherical indicatrix. mk4 bora headlightsWebFeb 15, 2024 · By using these associated curves, we give some methods to construct helices and slant helices from some special spherical curves such as circles on unit sphere, spherical helices, and spherical slant helices. Finally, we give some related examples. Introduction The study of curves has wide range applications in many areas. mk4 carbon fiberWebMar 24, 2024 · Tangent Indicatrix -- from Wolfram MathWorld Calculus and Analysis Differential Geometry Differential Geometry of Curves Tangent Indicatrix Let the speed of a closed curve on the unit sphere never vanish. Then the tangent indicatrix, also called the tantrix, is another closed curve on . If immerses in , then so will . Explore with Wolfram Alpha mk4 coachWebMar 24, 2024 · Let the speed sigma of a closed curve on the unit sphere S^2 never vanish. Then the tangent indicatrix, also called the tantrix, tau=(sigma^.)/( sigma^. ) is another … mk4 bora front bumperWebOct 1, 2005 · The spherical indicatricies of slant helicesIn this section, we investigate spherical images the tangent indicatrix and binormal indicatrix of a slant helix. We obtain … mk4 city light bulbWebOct 1, 2005 · The spherical indicatricies of slant helices. In this section, we investigate spherical images the tangent indicatrix and binormal indicatrix of a slant helix. We obtain … mk4 automatic shift cableWebJan 10, 2024 · In this paper, we calculate the Gaussian curvatures of the dual spherical indicatrix curves formed on unit dual sphere by the Blaschke vectors and dual instantaneous Pfaff vectors of dual parallel equidistant ruled surfaces (DPERS) and we give the relationships between these curvatures. In addition to—in cases where the base curves of … mk4 coaching stock