I have worked out correctly that: $L = 0.5m [h^2\Omega ^2 + a^2\dot{\theta}^2 + a^2\Omega^2sin^2\theta + 2ah\Omega\dot{\theta}cos{\theta} - 2gacos\theta]$
$\theta$ is the generalised coordinate and $a,g,h$ constants
However I'm having difficulty finding out what $a\ddot{\theta}$ is using the formula $\frac{d}{dt}\left(\frac{\partial L}{\partial \dot{\theta}}\right) - \frac{\partial L}{\partial \theta} = 0$
since when differentiating the right bracket I get $m[a^2\Omega^2sin\theta cos\theta - ah\Omega \dot{\theta}^2sin\theta + ah\Omega\ddot{\theta}cos\theta + ga\dot{\theta}sin\theta]$ which I'm sure is wrong.
The final answer is meant to be:
$a\ddot{\theta} = a\Omega^2sin\theta cos\theta +gsin\theta$
Any help greatly appreciated
What did you get for your partial derivatives... $$ \frac{\partial L }{\partial{\theta}} = 0.5m[a^2\Omega^2 2\sin\theta \cos\theta + 2ah\Omega\dot\theta(-\sin\theta)+2ga\sin\theta] $$ $$ \frac{\partial L}{\partial \dot{\theta}}=0.5m[a^22\dot\theta+2ah\Omega\cos\theta] $$
Next, differentiate wrt $t$.