Results 1 to 2 of 2

Math Help - Reparametrize a helix

  1. #1
    MHF Contributor arbolis's Avatar
    Joined
    Apr 2008
    From
    Teyateyaneng
    Posts
    1,000
    Awards
    1

    Reparametrize a helix

    Hi,
    I'm learning about reparametrizing curves and I don't understand what my teacher did in the following example :
    Reparametrize the helix (\cos t, \sin t, t) from (1,0,0) in the same direction than t increases.
    Solution: s(t)=\int_0^t |r'(u)| du.
    Then she continues from this and I understand all she did.
    What I don't understand is why the lower bound of the integral is 0.
    It's sometimes different from 0, so how do I know what lower bound to chose? I'm sure it's because of the (1,0,0) point, but why 0 as lower bound? Is it because the z-coordinate is worth 0 in (1,0,0)?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271

    think time

    You are reparameterizing in terms of arc length so s(t) is the distance traveled in time t.

    In most instances you are at the initial point when t= 0 which is why the bottom limit is 0. you are at the point (1,0,0) at t = 0. It has nothing to do with the spatial coordinates but rather the time coordinate.

    If for instance you were at the initial point (1,0,0) at t= t0 then t0 would be the lower limit of integration
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Helix, arc tangent envelope
    Posted in the Geometry Forum
    Replies: 0
    Last Post: November 9th 2010, 09:01 PM
  2. Helix
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 16th 2010, 03:26 AM
  3. Reparametrize a curve
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 17th 2009, 02:21 PM
  4. length of a helix
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 26th 2008, 08:06 PM
  5. [SOLVED] radius of a helix
    Posted in the Calculus Forum
    Replies: 0
    Last Post: February 28th 2008, 04:04 AM

Search Tags


/mathhelpforum @mathhelpforum