1
$\begingroup$

I encountered the following differential equation when I tried to derive the equation of motion of a simple pendulum:

$\frac{\mathrm d^2 \theta}{\mathrm dt^2}+g\sin\theta=0$

How can I solve the above equation?

  • 3
    The solution involves Jacobi's elliptic function "sn". There is a (very sketchy) description of how to integrate the equation at http://www.mai.liu.se/~halun/complex/elliptic/.2012-02-01
  • 0
    you can solve a small angle approximation by assuming $\sin\theta\approx\theta$2012-02-01
  • 0
    @yoyo Can't it be done without the small angle approximation? I wanted to derive a general equation for all cases. Anyways I don't know how to solve even with the approximation, so it'll be helpful even if you explain that method.2012-02-01

3 Answers 3