3. Consider the model of the uncontrolled inverted pendulum 3 (4-3 cos ) +$ sin 26- 6g - sin = 0 1 'm, e (a) Determine the stable and unstable manifolds of the saddle equilibria up to third order. (b)) Consider g= 10 [m/s] and /= 1 [m] and plot the results obtained in part (a). Show that the obtained analytical results correspond to the manifolds obtained by numerical simulations.