Results 1 to 4 of 4

Math Help - Radius of curvature problem

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    114

    Radius of curvature problem

    I'm having a little trouble finding the radius of curvature for problems of the following form

    y^n=f(x)

    For examples. I'm asked to find the radius of curvature at the point (0,0) for the curve y^2=4ax

    So

    2y\, y' = 4a \implies y' = 2ay^{-1}

    and

    y'' = -2ay^{-2}\, y'

    So

    \rho = \frac{[1+(y')^2]^{\frac{3}{2}}}{y''} = \frac{[1+4a^2y^{-2}]^{\frac{3}{2}}}{-2ay^{-2}\, y'}

    it's at this point where I'm sure I've messed up. If anyone could tell me how to solve these types of questions I'd be very grateful

    Regards

    Stonehambey
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    This is a parabola.

    Let y=t, then x=\frac{t^{2}}{4ax}

    and {\kappa}(t)=\frac{\frac{1}{|2a|}}{[\frac{t^{2}}{4a^{2}}+1]^{\frac{3}{2}}}

    t=0 \;\ when \;\ (x,y)=(0,0), \;\ so \;\ {\kappa}(0)=\frac{1}{|2a|}, \;\ {\rho}=2|a|
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2008
    Posts
    114
    Quote Originally Posted by galactus View Post
    This is a parabola.

    Let y=t, then x=\frac{t^{2}}{4ax}

    and {\kappa}(t)=\frac{\frac{1}{|2a|}}{[\frac{t^{2}}{4a^{2}}+1]^{\frac{3}{2}}}

    t=0 \;\ when \;\ (x,y)=(0,0), \;\ so \;\ {\kappa}(0)=\frac{1}{|2a|}, \;\ {\rho}=2|a|
    Hi, thanks for the reply, but I'm afraid I cannot follow your answer (and I would very much like to, since it's correct). Would you mind explaining the steps at all?

    Regards,

    Stonehambey
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Nov 2008
    Posts
    114
    Ah, so I did a little reading this morning, and I can now work through it parametrically. However this question was in the exercise right after the cartesian method had been explained, the parametric method hadn't even been covered yet. The logical conclusion is that you can solve this using cartesian method. But I'm not sure how since I keep getting situations where I'm dividing by zero!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Acceleration and radius of curvature
    Posted in the Calculus Forum
    Replies: 0
    Last Post: August 25th 2010, 04:47 PM
  2. Radius of Curvature
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 11th 2010, 12:26 PM
  3. What is the instantaneous radius of curvature?
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: November 11th 2009, 03:37 AM
  4. nstantaneous radius of curvature
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 5th 2009, 12:09 AM
  5. radius of curvature
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 8th 2007, 11:07 AM

Search Tags


/mathhelpforum @mathhelpforum