Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help with reparameterizing

  1. Feb 14, 2004 #1
    I think that i'm just having problems with my derivitives and integrals. If someone one could show me what the steps of this problem look like it would be greatly appreciated. "Reparameterize the curve with respect to the arc length measured from the point where t=0 in the direction of increasing t. r(t)=e^t*sint i +e^t*cost j"
     
  2. jcsd
  3. Feb 14, 2004 #2

    HallsofIvy

    User Avatar
    Science Advisor

    Looks like homework to me!

    Step 1: If you want to use arc-length as a parameter, then you will need to know what the arc-length is! The formula for arclength, given x and y in terms of parameter t, taking t= 0 as starting point and t>0 as positive arclength, is:
    [tex]s(t)= \int_0^t\sqrt{x'^2+y'^2}dt[/tex].

    Step 2: That will give you arclength, s, as a function of t. Now solve for t as a function of s and substitute that formula into your parametric equations.
     
    Last edited by a moderator: Feb 15, 2004
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook