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