Compute the curvature k and torsion of the curve

| August 31, 2017

Question
1..) Compute the curvature k and torsion.png”> of the curve

α(t) = (a cos2(t), a sin(t) cos(t), a sin(t)).

Then, for a = 1, graph α(t) and the sphere of radius 1 centered at the origin on the same set of axes. Also, show that the curve α(t) is a spherical curve by computing

(.png”>)2 + (.png”> (.png”>)’.png”>)2

To be a constant (which must be the squared radius of the sphere on which α lies). Note that the extra
|.png”> | = ds/dt is necessary since α is not unit speed and the derivative of 1/k here is with respect to t whereas the derivative of 1/k above was with respect to arclength s.Use maple anduse formulas Non-Speed Curves.

*** Hints: Explain why the formula for a spherical curve here looks different from that of exercise 1**

Exercise.1**)Show that, if (.png”> )’.png”>0 and (.png”>)2 + ((.png”> )’.png”>2 is a constant, then a ( unit speed) curve α lies on a sphere.

I did the question by maple but here please I want just answer the hintsExplain why the formula for a spherical curve here looks different from that of exercise 1**
(highlight formula) please explain that very clear.

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