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Math Help - Unit tangent, normal, binormal etc.

  1. #1
    Junior Member SirOJ's Avatar
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    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

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  2. #2
    MHF Contributor Calculus26's Avatar
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    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)||
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  3. #3
    Junior Member SirOJ's Avatar
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    Quote Originally Posted by Calculus26 View Post
    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...?
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