(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the unit speed curve alpha(s) with k(s)=1/(1+s^2) and tau defined as 0.

2. Relevant equations

Use the Frenet-Serret equations

K(s) is the curvature and tau is the torsion

T= tangent vector field (1st derivative of alpha vector)

N= Normal vector field (T'/k(s))

B= Binormal vector field (T x N)

K(s) is defined as the norm of T'

3. The attempt at a solution

Ok I wrote out the matrix for the Frenet-Serret and found the differential equations to solve:

T' = T/(1+s^2) *which implies => (alpha(s))'' = (alpha(s))'/(1+s^2)

N'= -N/(1+s^2) *which implies =>N' = -(alpha(s)''/(1+s^2)

B'=0

Which so far is really quite easy. But here is the kicker, when I try to solve the diff. eq's and go back and check my solutions, my k(s) value is not correct. I feel rather stupid for asking this, but I seem to have forgotten how to treat a systems of diff. eqs. Any thing to kick start my memory for solving this system would be great.

Thanks for any help in advanced.

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# Homework Help: Solving for a unit speed curve given curvature and torsion (diff. geo)

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