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

Parameterizing an equation?

  1. Feb 17, 2012 #1

    Fuz

    User Avatar

    How do you take an equation and turn it into a parametric one? Eliminating the parameter is straightforward and easy; but I'm trying to go the other way.

    e.g. what steps would one take to convert some curve like

    y = x2

    or

    x2 + y2 = 1

    into parametric equations with 't' as the independent variable?
     
  2. jcsd
  3. Feb 17, 2012 #2
    There are number of ways, for conics, some traditional ways are:
    For y=x2; x=t, y=t2.
    For x2+y2=1; x=cost, y=sint.
     
  4. Feb 17, 2012 #3

    Fuz

    User Avatar

    What was your motivation for setting x = cos(t) and y = sin(t)? Is there a method for turning an equation in to a set of parametric equations?
     
  5. Feb 17, 2012 #4
    actually, eliminating the parameter is equally hard. If the equation is in an explicit form [itex]y = f(x)[/itex], then, whatever you take as a parametric representation of x, [itex]x = \phi(t)[/itex], you can find [itex]y = y \left[ \phi(t) \right] = \psi(t)[/itex]. In other cases, there is no general rule. For example, eliminate the parameter in:
    [tex]
    x = t \, \cos t, \ y = t \, \sin t
    [/tex]
    describing an Archimedian spiral.
     
  6. Feb 18, 2012 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You hopefully have learned that [itex]cos^2(t)+ sin^2(t)= 1[/itex]. Comparing that to [itex]x^2+ y^2= 1[/itex] should make the parameterization obvious. But there is no general way of parameterizing (except that if y= f(x), you can always use x= t, y= f(t)).
     
  7. Feb 18, 2012 #6

    chiro

    User Avatar
    Science Advisor

    Hey Fuz.

    On top of what the other posters have said, it does help immensely if you know the dimension of the system.

    If you are dealing with a one-dimensional system (like a line), then there are techniques that you can do to make a move towards getting a complete analytic parametrization.
     
  8. Feb 18, 2012 #7

    Fuz

    User Avatar

    Yes I have learned this, and that basically answered my question, but then what is the point in just setting x equal to t?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Parameterizing an equation?
  1. Parameterizing a shape (Replies: 1)

  2. An equation (Replies: 8)

Loading...