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Symplectic integrators of the pendulum equation?

  1. May 21, 2012 #1
    In particular, a symplectic integrator to solve:

    [itex]\ddot{\theta} + \dfrac{g}{l} \sin(\theta) = 0[/itex]

    I'm currently using velocity verlet - by realizing that

    [itex]\ddot{\theta} = -\nabla (-cos(\theta)) = A(\theta(t))[/itex]

    ie. letting x = theta
    v = dtheta/dt
    a = d^2 theta /dt^2

    is it safe to apply verlet integration to generalized coordinates? In particular, does this hold true for a generalized coordinate theta:

    [itex]\theta_{t+dt} \approx \theta_t + \dot{\theta}_t dt + \frac{1}{2} \ddot{\theta}_t (dt)^2[/itex]
     
    Last edited: May 22, 2012
  2. jcsd
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