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- #1

- Aug 30, 2012

- 1,180

\(\displaystyle \ddot{ \theta} = A~\cos( \theta )\)

and

\(\displaystyle \dot{ \theta } ^2 = B( \sin( \theta ) - \sin( \theta _0 ) )\)

where the dot represents a time derivative and \(\displaystyle \theta _0\) is the angle at time t = 0. (This is the harmonic oscillator where the angle is not taken to be small. A and B are related constants and I can give the derivations if you feel you need them.)

I'm looking for an iterated solution for \(\displaystyle \theta (t)\), but I'm actually more interested in \(\displaystyle t( \theta )\) for now.

Most of the Physics is involved with the first equation, which you are more likely to find as \(\displaystyle \ddot{ \theta } = A~\sin( \theta )\) if you look it up. The second equation can be taken simply to mean that \(\displaystyle \sin( \theta _0 ) \leq \sin( \theta )\) at all times.

Thanks for any help!

-Dan