Question

2) Let C be the curve given by unit speed parametrization $\vec{x}(s)$, the curvature $\kappa(s)$, torsion $\tau(s)$ and Frenet Frame $(\vec{T}(s), \vec{N}(s), \vec{B}(s))$. Then the binormal indicatrix is given by $\vec{x}(s) = \vec{B}(s)$. Find the curvature and torsion of the binormal indicatrix.

Name: 2 let c be the curve given by unit speed parametrization vecxs the curvature kappas torsion taus and frenet frame vects vecns vecbs then the binormal indicatrix is given by vecxs vecbs find 28122
Uploaded: 2020-09-05T11:56:50-08:00
Duration: 1 min 55 s
Channel: Tanishq Gupta
Description: 2 let c be the curve given by unit speed parametrization vecxs the curvature kappas torsion taus and frenet frame vects vecns vecbs then the binormal indicatrix is given by vecxs vecbs find 28122

          2) Let C be the curve given by unit speed parametrization $\vec{x}(s)$, the curvature $\kappa(s)$, torsion $\tau(s)$ and Frenet Frame $(\vec{T}(s), \vec{N}(s), \vec{B}(s))$. Then the binormal indicatrix is given by
$\vec{x}(s) = \vec{B}(s)$.
Find the curvature and torsion of the binormal indicatrix.

2 let c be the curve given by unit speed parametrization vecxs the curvature kappas torsion taus and frenet frame vects vecns vecbs then the binormal indicatrix is given by vecxs vecbs find 28122

Added by Matthew W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Tanishq Gupta

09/05/2020

Step 1

We want to find the curvature and torsion of this curve. The tangent vector of $\vec{x}(s)$ is given by $\vec{x}'(s) = \vec{B}'(s)$. From the Frenet-Serret formulas, we have $\vec{B}'(s) = -\tau(s)\vec{N}(s)$. Thus, the tangent vector is $\vec{T}_B(s) = Show more…

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2) Let C be the curve given by unit speed parametrization $\vec{x}(s)$, the curvature $\kappa(s)$, torsion $\tau(s)$ and Frenet Frame $(\vec{T}(s), \vec{N}(s), \vec{B}(s))$. Then the binormal indicatrix is given by $\vec{x}(s) = \vec{B}(s)$. Find the curvature and torsion of the binormal indicatrix.