Let . At , find

(i) the unit tangent vector T,

(ii) the unit normal vector N,

(iii) the curvature κ,

(iv) the binormal vector B,

(v) the torsion

I'll come back to this one with my thoughts on it.

For the moment, I must go catch some shuteye...

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- December 1st 2009, 09:40 AMUnenlightenedUnit tangent vectors
Let . At , find

(i) the unit tangent vector T,

(ii) the unit normal vector N,

(iii) the curvature κ,

(iv) the binormal vector B,

(v) the torsion

I'll come back to this one with my thoughts on it.

For the moment, I must go catch some shuteye... - December 1st 2009, 10:44 AMadkinsjr
If you were given this problem, surely you were shown how to find these. There's really nothing to it. It's just direct application of the theorems and definitions. You should know how to find the derivative of a vector and the unit tangent vector at any point is just .

The curvature

Just find the definitions in the book and apply them. Like I said, you don't really have to think about much to do these excercises. - December 2nd 2009, 05:39 AMUnenlightened
- December 2nd 2009, 07:28 AMHallsofIvy
Differentiate with respect to t. The normal vector is the vector of unit length pointing in the direction of that derivative vector.

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(ii) the unit normal vector N,

**is**the arclength as a function of t. If you can solve for t as a function of s, differentiate the unit tangent vector with respect to**s**to get a normal vector. Divide by the length of that to get the unit normal vector.

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(iii) the curvature κ,

**is**the curvature.

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(iv) the binormal vector B,

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(v) the torsion

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I'll come back to this one with my thoughts on it.

For the moment, I must go catch some shuteye...