Spherical indicatrix
WebIndicatrix. in optics a vector diagram representing the dependence on direction of the characteristics of a light field (light intensity and polarization) or of the optical characteristics of the medium (indexes of refraction; reflectivity). A particular case of the indicatrix is the scattering indicatrix, which represents the dependence of the ... WebAug 5, 2015 · In this paper Fermi–Walker derivative and Fermi–Walker parallelism and non-rotating frame concepts are given along the spherical indicatrix of a timelike curve in …
Spherical indicatrix
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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
WebJun 6, 2024 · The tangent indicatrix $ T $ of any regular curve in $ \mathbf R ^ {n} $ thus traces out a curve on the unit sphere $ S ^ {n - 1 } \in \mathbf R ^ {n} $ which, as a point set, is independent of the parametrization of $ \gamma $. ... B. Solomon, "Tantrices of spherical curves" Amer. Math. Monthly, 103 : 1 (1996) pp. 30–39 [a3] WebDec 31, 2013 · The first Bishop spherical indicatrix and the second Bishop spherical indicatrix are denoted by and separately. The first type-2 Bishop spherical indicatrix and the second type-2 Bishop spherical indicatrix in [7] is denoted by and separately. 3. Cusps of Bishop Spherical Indicatrixes and Their Visualizations
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 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 some new characterizations of curvatures in terms of some partial differential equations.
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 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. rutherford merlotWebApr 13, 2024 · I'm trying to find the curvature and torsion of the tangent indicatrix of a curve with respect to the curvature and torsion of the initial curve, that is, if $\kappa, \tau$ are the curvature and torsion of $\alpha(s)$, what is the curvature and torsion of $\beta(s) = \alpha'(s)$? I'm aware of The curvature and torsion of the tangent indicatrix rutherford mentorWebIn differential geometry, the tangent indicatrix of a closed space curve is a curve on the unit sphere intimately related to the curvature of the original curve. Let γ ( t ) {\displaystyle … is china porcelain or ceramic