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Thread: Curvature Formula

  1. #1
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    Curvature Formula

    Find curvature given r (t) = e^t*cost i + e^t*sint j.

    There are two formulas but I was told to avoid using the formula that does not involve the cross product when no value for the parameter t is given.

    Formulas:

    1. K = ||r'(t) X r"(t)||/||r'(t)||^3

    2. K = ||T' (t)||/||r'(t)||

    Which formula is "easier" to apply in this case and/or in most cases? I was told to apply formula (1) for polynomials. What about for problems involving e^t, lnx and trigonometric functions?
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  2. #2
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    Re: Curvature Formula

    Hey USNAVY.

    It should depend on whether you have T(t) and r(t) or just r(t).
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  3. #3
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    Re: Curvature Formula

    Quote Originally Posted by chiro View Post
    Hey USNAVY.

    It should depend on whether you have T(t) and r(t) or just r(t).
    I gave up on this question after several attempts to solve it. I came very close to getting the right answer yesterday but failed. My answer is K = e^(-t)/(cos t)^2. The right answer is (sqrt {2}/2)(e^(-t). Can you solve it step by step?I want to see the proper steps and use your solution to solve similar questions in my textbook.
    Last edited by USNAVY; Jan 9th 2017 at 07:34 AM.
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  4. #4
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    Re: Curvature Formula

    We usually get the poster to show their working before we give them more advice.
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  5. #5
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    Re: Curvature Formula

    Quote Originally Posted by chiro View Post
    We usually get the poster to show their working before we give them more advice.
    I will post my work tomorrow.
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