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Math Help - Curve parametrizations

  1. #1
    Junior Member SirOJ's Avatar
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    Curve parametrizations

    Find the vectors
    T, N and B as well as the curvature  and the torsion  for the curve


    r
    (t) = e^t cos t i + e^t j + e^t sin t k

    I calculated e^t = (4/3)s.. Is there any way i can get t = "something" from this equation because i need to parametrize the above curve in terms of the arc length "s"
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  2. #2
    MHF Contributor

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    Quote Originally Posted by SirOJ View Post
    Find the vectors
    T, N and B as well as the curvature  and the torsion  for the curve


    r
    (t) = e^t cos t i + e^t j + e^t sin t k

    I calculated e^t = (4/3)s.. Is there any way i can get t = "something" from this equation because i need to parametrize the above curve in terms of the arc length "s"
    Well, yes! If e^t= (4/3)s then t= ln((4/3)s which you can, if you like, write as t= ln(s)+ ln(4/3)= ln(s)+ ln(4)- ln(3).
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