# Unit tangent, normal, binormal etc.

• Dec 4th 2009, 02:10 AM
SirOJ
Unit tangent, normal, binormal etc.
Find the vectors

T, N and B as well as the curvature and the torsion of;

r(t) = (t^3)/3i + (t^2)/2j for t>0

I parametrized the curve and got
r(s) = ((3s+1)^2/3 - 1)^3/2)/2i + ((3s+1)^2/3 - 1)/2i

and I then proceeded to find T(s) for which I calculated;

T(s) = (3s+1)^5/3((3s+1)^2/3 - 1)^5/2)i + (3s+1)^5/3j

Is this the right answer? or Am i going the right way about it this at all...? because using this answer for the unit tangent vector its going to take me ages to calculate N, B, curvature & torsion..

Any help would be greatly appreciated

• Dec 4th 2009, 04:20 AM
Calculus26
No need to reparameterize

T = r'(t)/||r'(t)||

N = T '(t)/||T'(t)||

B = T x N

The curvature can be computed by k = ||T'(t)||/||r'(t)||
• Dec 4th 2009, 04:30 AM
SirOJ
Quote:

Originally Posted by Calculus26
No need to reparameterize

T = r'(t)/||r'(t)||

N = T '(t)/||T'(t)||

B = T x N

The curvature can be computed by k = ||T'(t)||/||r'(t)||

Cheers for the help..

In our class notes we were given the formula's for T,N,B,k etc. using reparametrizations.. so i'm not sure how happy lecturere would be using a different method.. Although i guess a correct answer is a correct answer no matter how you get it...?