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Need some help with nonlinear integration

  1. Nov 21, 2004 #1

    I study animation, and I wanted to make a script where I can automate pendulums in my scene with some kind of realistic physics, rather than animate them manually.

    So 'right' I think, 'I need to go study some physics and maths' - but it wasnt as easy as I hoped, Ive hit a wall, and it is the nonlinear integration of the second order D.E:

    y" = -(g/L)sin(y)

    So from my limited understanding, this equation is non-linear due to the absence of y', and because y is a function of sin.

    Its seems the only hints Ive been able to get is that integrating it is not a particually easy thing to do, with references only giving me parameters to enter into mathematics software for computation.The problem is, I essentially need to write my own software(script), and without understanding what is going on, I cant.

    If I could get some better idea of what is involved, then I can decide if its going to be worth my while spending more time trying to do this now, or if I need a diploma in advanced mathematics first :)

  2. jcsd
  3. Nov 21, 2004 #2


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    Non linear problems are best dealt with numerically. If you must solve the nonlinear equation look into a Runga Kutta method. If you keep the oscillations of your pendulum small (< .2 rad or ~10deg) you can use the usual approach and let sin [itex] \Theta [/itex] = [itex] \Theta [/itex] then the problem is linear and easily solved.
  4. Nov 21, 2004 #3
    Thankyou Integral, I will look into the Runga-Kutta method.

    I would like to be able to calculate large angle pendulums, upto 180 degrees, so unfortunatly(for me) I cannot linearise the equation.
  5. Nov 21, 2004 #4


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    You should, however, integrate once:
    Multiply your equation with y':
    Integrated from t=0 to some arbitrary t-value, you get:
    Last edited: Nov 21, 2004
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