Consider a curve C in 3D space given by the vector function r(t) = where a, b, and c are constants. Determine the curvature κ(t) of the curve C at any point t.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider a curve C in 3D space given by the vector function r(t) = <a sin(t), b cos(t), ct> where a, b, and c are constants.

Determine the curvature κ(t) of the curve C at any point t.

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Step 1: Solution

Given vector function: r left parenthesis t right parenthesis equals open angle brackets a sin t comma space b cos t comma space c t close angle brackets

where a comma space b and c are constants.

We have to determine the curvature k left parenthesis t right parenthesis of the curve c at any point t.


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