Results 1 to 2 of 2

Thread: Curvature

  1. #1
    Junior Member
    Joined
    Dec 2008
    Posts
    62

    Curvature

    Compute explicitly a plane curve $\displaystyle c(s) $ which is parameterized by arc length and whose curvature is $\displaystyle \kappa(s) = s^{-\frac{1}{2}} $.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by mathman88 View Post
    Compute explicitly a plane curve $\displaystyle c(s) $ which is parameterized by arc length and whose curvature is $\displaystyle \kappa(s) = s^{-\frac{1}{2}} $.
    we have $\displaystyle c(s)=(x(s), y(s)),$ where $\displaystyle x'(s)=\cos \theta, \ y'(s)=\sin \theta,$ where $\displaystyle \frac{d \theta}{d s} = \kappa = \frac{1}{\sqrt{s}}.$ thus one solution would be $\displaystyle \theta = 2\sqrt{s}$ and so $\displaystyle x'(s)=\cos(2\sqrt{s}), \ y'(s)=\sin(2\sqrt{s}).$

    now integrate (substitute $\displaystyle 2\sqrt{s}=t$ and then use by parts) to find $\displaystyle x(s)$ and $\displaystyle y(s).$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Curvature
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Feb 28th 2010, 03:36 PM
  2. Curvature
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Sep 22nd 2009, 10:42 AM
  3. curvature
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Sep 20th 2009, 07:29 PM
  4. Curvature
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: May 4th 2009, 04:29 PM
  5. curvature
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Apr 28th 2009, 12:35 PM

Search Tags


/mathhelpforum @mathhelpforum