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

Boundary value problem(ODEs)

  1. Nov 29, 2009 #1
    Dear everybody,

    I am new here. I need your suggesstion and helping for solving the next nonlinear boundary value problem:

    with x(0)=y(0)=-1 and x(pi/4)=y(pi/4)=1

    so is it easy to get the analytical solution to the problem above or I have to solve this problem numerically.
    thanks in advance

    Last edited: Nov 29, 2009
  2. jcsd
  3. Nov 29, 2009 #2
    Using polar coordinates, and rewriting in vector form you get the equivalent equation:

    [tex]\frac{d\vec{r}}{dt}=\hat{\theta}[/tex] (1)


    Putting this in the equation (1) and comparing different components you get:

    [tex]\frac{dr}{dt}=0 => r(t) \equiv const=R[/tex]
    [tex]r\frac{d\theta}{dt}=1 [/tex]

    Since r is constant you get:

    [tex] \theta=\frac{t}{r}+\varphi [/tex]

    From this you get that:

    [tex] x(t)=Rcos(\frac{t}{R}+\varphi); y(t)=Rsin(\frac{t}{R}+\varphi); [/tex]

    You have a circular motion with a radius and initial phase to determine from boundry conditions.
    Last edited: Nov 30, 2009
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook