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Math Help - How to solve this System of Second Order Differential Equations (DE) with IVP

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    How to solve this System of Second Order Differential Equations (DE) with IVP

    Hello, I'm trying to figure out how solve the below for varying time and/or corresponding theta. I'm stumped.. any insight is greatly appreciated. Thank you

    \ddot{R} = −\alpha|v|\dot{R} - \beta_{s}\frac{|v|}{R}\dot{R}-\beta_{c}\frac{g}{|v|}\dot{R} + [R\dot{\theta}^2-\frac{5}{7}g(tan\delta cos\varepsilon -sin\varepsilon cos\theta]cos^2\delta

    \ddot{\theta} = −\alpha|v|\dot{\theta} - \beta_{s}\frac{|v|}{R}\dot{\theta}-\beta_{c}\frac{g}{|v|}\dot{\theta}- 2\dot{R}\dot{\theta}/R - \frac{5}{7}\frac{g}{R}sin\varepsilon sin\theta

    with |v|=\sqrt{\dot{R}^2/cos^2\delta + R^2\dot{\theta}^2}

    where
    \alpha = 0.00900350489819847
    \beta_{s} = 0.0022919958783044724
    \beta{c}=0.0062192039382357378
    \delta=0.2574
    R=0.242
    g=9.807

    with the 'initial conditions' at t = 0:

    R(0) = R
    \dot{R}(0) = 0
    \theta(0) = 57.899552605659885
    \dot{\theta}(0) = 2.7371516764119637

    This is modeling a ball rolling inside of a cone with the tip of the cone facing down. So the ball starts off at the rim of the cone and spins around inside the cone going further and further towards the tip. A good example of this is to think about a roulete ball which is spinning around the rim of the roulette table and then slowly approachs the spinning numbers in the middle. As the ball slows down, gravity takes over and it approachs the center (tip) of the cone faster and faster.
    Last edited by kashyappatel7; June 15th 2012 at 09:46 PM.
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