(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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**