Lyapuniv-functions
We have the system of ODEs
$y_1'= y_2$
$y_2'=-y_2-\sin(y_1)$.
Decide for each of the following functions whether it is a Lyapunov-function of $(0,0)$ or not:
$V(y_1,y_2)= y_1^2+y_2^2$.
$V(y_1,y_2)= \frac{y_2^2}{2}+(1- \cos(y_1))$.
$V(y_1,y_2)= \frac{(y_1+y_2)^2}{2} + y_1^2 + \frac{y_2^2}{2}$.
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