Pendulum with quadratic damping
= Pendulum with quadratic damping
{title2=$\ddot\theta+c\dot\theta|\dot\theta|+\sin\theta=0$}
In nondimensional time the <quadratic damping> removes energy from the pendulum at rate $-c|\omega|^3$. Downward resting positions are nonhyperbolic asymptotically stable spirals, even though the linearized equation has a centre. Upward resting positions remain <saddle equilibria>. Each fixed-sign branch of $\omega$ has a linear equation for $\omega^2$ as a function of angle.