Find the curvature of the curve: R(t) = (2sint, t, 2cost)Findne ac

Introduction: The formula of the curvature of any curve is given by, κ=R'(t)×R"(t)R'(t)3 Where Rt is…

Answered: Find the curvature of the curve: R(t)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Find the curvature of the curve: R(t) = (2sint, t, 2cost)
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Expert Solution

Step 1

Introduction:

The formula of the curvature of any curve is given by,

$\begin{array}{rcl} κ & = & \frac{||R' (t) \times R " (t)||}{{||R' (t)||}^{3}} \end{array}$

Where $R (t)$ is any curve parametrized by t.

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Follow-up Question

In the last step of the solution you have 2sqrt(5)/(sqrt(5))². Isn't that supposed to be 2sqrt(5)/(sqrt(5))³? It is cubed in the original equation for curvature so was wondering if that was just a typo in the solution or if there is a reason the denominator is squared instead of cubed?

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