I’ve been stuck on this problem for absolutely ages.
I’ve got the equation $$\theta’’(t)+c\theta’(t)+sin\theta=0$$ And by writing it as a system of equations for $x(t)=\theta$ and $y(t)=\theta’$ I need to find all the stationary points and their nature (for all c except c=2)
I solved for x’=0 and y’=0 which got me the set of points $(2n\pi,0)$. I thought my next step would be to form the hessian matrix. But in this context I don’t know how I’d do that.