Results 1 to 3 of 3

Math Help - curved formed by the intersection of two equal cylinders.

  1. #1
    Senior Member
    Joined
    Jan 2008
    From
    Montreal
    Posts
    311
    Awards
    1

    curved formed by the intersection of two equal cylinders.

    I'm wondering if anybody can help me solve the following problem, the curve I'm getting at the end is either planar or is completely incorrect.

    Find the curvature and the parametrized curved formed by intersection the following two cylinders:

    x^2+(y-1)^2=1
    y^2+z^2=1

    so what I have after some calculation is:

    x=\pm \sqrt{1-(\sqrt{1-z^2}-1)^2}

    y=\sqrt{1-z^2}

    Now if I convert let z=\sin(t) and substitute then the result follows. But is there a way that I don't have to deal with both positive and negative parts of the equation, as to simplify the curvature calculation?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    Quote Originally Posted by lllll View Post
    But is there a way that I don't have to deal with both positive and negative parts of the equation, as to simplify the curvature calculation?
    You can use the Implicit Function Theorem if you want to find the curvature.

    For example, express \vec{r}(t)=(x(t),y(t),t) and you'll obtain \vec{r}\;'(t)=((y-1)z/xy,-z/y,1) if xy\neq 0 etc.


    Fernando Revilla
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jan 2008
    From
    Montreal
    Posts
    311
    Awards
    1
    thanks, that thought hasn't occured to me.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Intersection of Three cylinders
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 16th 2011, 06:21 PM
  2. Replies: 2
    Last Post: September 19th 2011, 07:10 AM
  3. Intersection of a ray and a curved surface
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 30th 2010, 11:45 AM
  4. Cylinders - how many can be formed?
    Posted in the Geometry Forum
    Replies: 3
    Last Post: February 9th 2010, 03:28 PM
  5. Replies: 1
    Last Post: October 1st 2008, 09:05 AM

Search Tags


/mathhelpforum @mathhelpforum