Results 1 to 6 of 6

Math Help - Finding curvature

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    12

    Finding curvature

    Find the curvature K of the curve.
    r(t) = < e^t cos(t) , e^t sin(t) , e^t >

    I have:
    <br />
r(t) = < e^t cos(t) , e^t sin(t) , e^t >
    r'(t) = < e^t cos(t) - e^t sin(t), e^t sin(t) + e^t cost(t), e^t ><br />
    r''(t) = < - e^t cos(t) - e^t sin(t) + e^t cos(t) - e^t sin(t) , <br />
     e^t cos(t) + e^t sin(t) + e^t cos(t) - e^t sin(t), e^t ><br />

    Combine like terms:
    <br />
r''(t) = <- 2e^t sin(t) , 2e^t  cos(t) , e^t ><br />

    I have that curvature is

    <br />
\kappa = \frac{|r' \times r''|}{|r'|^3}<br />

    For the numerator I crossed r' and r'' and got:

    <br />
<e^{2t} [sin(t)-cos(t)], -e^{2t} [sin(t)+cos(t)], 2e^{2t}><br />

    I don't know how to convert this into a magnitude; same for denominator.
    Last edited by Negativ; June 10th 2010 at 11:06 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    The magnitude of a vector |\vec{v}|=\sqrt{\vec{v}\cdot\vec{v}}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2010
    Posts
    12
    I got down to \frac{root{2}}{3e^t}

    That look right? :/
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    Can you clean up the LaTeX code a bit?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2010
    Posts
    12
    Tried to make it more legible.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    Try this: \frac{\sqrt{2}}{3e^{t}}. You can click on the equation I just wrote down to see what LaTeX code I wrote to obtain it.

    That's what I got as well. Looks good!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Curvature
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 23rd 2011, 02:00 PM
  2. Finding the Curvature K
    Posted in the Calculus Forum
    Replies: 11
    Last Post: October 29th 2010, 09:17 PM
  3. Finding center and circle of curvature
    Posted in the Calculus Forum
    Replies: 0
    Last Post: March 22nd 2010, 11:45 AM
  4. Replies: 5
    Last Post: January 25th 2010, 08:43 AM
  5. Finding the curvature of a distorted manifold
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: December 17th 2008, 04:42 PM

Search Tags


/mathhelpforum @mathhelpforum