Results 1 to 2 of 2

Math Help - Tangent and normal vectors for an ellipse

  1. #1
    psd
    psd is offline
    Newbie
    Joined
    Oct 2009
    Posts
    1

    Tangent and normal vectors for an ellipse

    I need to find unit normal and tangent vectors for an ellipse with major axis ( x) of length a and minor axis ( y) of length b.

    My initial guesses are
    \hat{N}=b\cos{\theta}\hat{i}+a\sin{\theta}\hat{j}
    and
    \hat{T}=-a\sin{\theta}\hat{i}+b\cos{\theta}\hat{j}

    These are orthogonal, but lead to incorrect results later so I suspect they're wrong.

    Anyone?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by psd View Post
    I need to find unit normal and tangent vectors for an ellipse with major axis ( x) of length a and minor axis ( y) of length b.

    My initial guesses are
    \hat{N}=b\cos{\theta}\hat{i}+a\sin{\theta}\hat{j}
    and
    \hat{T}=-a\sin{\theta}\hat{i}+b\cos{\theta}\hat{j}

    These are orthogonal, but lead to incorrect results later so I suspect they're wrong.

    Anyone?
    "Guesses"? Why guesses? Since your ellipse is  a\cos t\, i+b\sin t\, j\,,\; t\in [0,2\pi], derivating you get a tangent vector and thus a perpendicular vector to this first one is a normal to the ellipse...but you're forgetting, I'm afraid, that these vectors have to be of length 1 !

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: November 15th 2011, 05:10 PM
  2. Tangent of ellipse
    Posted in the Geometry Forum
    Replies: 4
    Last Post: April 28th 2010, 12:55 AM
  3. Tangent to an ellipse
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 24th 2010, 03:00 AM
  4. unit tangent and normal vectors
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 9th 2009, 11:34 AM
  5. About tangent to the ellipse
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 12th 2008, 03:57 AM

Search Tags


/mathhelpforum @mathhelpforum