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Math Help - Vector calculus

  1. #1
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    Vector calculus

    Let C be the circle of radius 3 centered at thepoint (2, 5) in the xy plane.

    a. Givethe arc-length parametrization of this curve
    b. Verify that the curvature is constant.


    thanks
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  2. #2
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    Re: Vector calculus

    a. Write down the polar representation of your circle. And just scale your parameter so as to get the arc length parametrization (instead of the angle parametrization)
    b. Trivially, a circle always has a constant curvature. But if your are really required to compute that curvature, the formula is

    \frac{\dot{x}\ddot{y}-\dot{y}\ddot{x}}{(\dot{x}^2+\dot{y}^2)^{3/2}}
    Last edited by jens; April 26th 2012 at 09:13 AM.
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