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Math Help - Curvature Problem (What Am I Doing Wrong?)

  1. #1
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    Curvature Problem (What Am I Doing Wrong?)

    Find the curvature "k" of r(t) = <-t+sint , 1+cost>

    I'm using the formula: (magnitude of cross product of a and v) / ((magnitude of velocity)^3)
    I got:
    v(t) = <-1+cost, -sint>
    a(t) = <-sint, -cost>
    mag. of cross prod. = 1+cost
    mag. of velocity = sqrt(2-2cost)
    k = (1+cost)/((2-2cost)^(3/2))

    This answer is not correct. What am I doing wrong?
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  2. #2
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Curvature Problem (What Am I Doing Wrong?)

    For curvature use:

    \kappa =\frac{x'(t) y''(t)-x''(t) y'(t)}{\left(x'(t)^2+y'(t)^2\right)^{3/2}}=

    =-\frac{1}{2 \sqrt{2-2 \text{cos}(t)}}
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  3. #3
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    Re: Curvature Problem (What Am I Doing Wrong?)

    Check your cross product again.
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