Consider the system
$$\begin{align} \dot{u}&= v\\ 147\dot{v}&=8150-588v-20000w\sin{u}\\ 330\dot{w}&=-135w+85\cos{u}+61 \end{align}$$
Find all equilibria where each $u,v,w\in[-\pi,\pi]$.
I can't see a nice way to solve this since there are no common terms in the second and third equation. There is also nonlinearity present which makes the resulting equations harder to solve.
equilibrium is when $$\begin{align} 0&= v\\ 0&=8150-588v-20000w\sin{u}\\ 0&=-135w+85\cos{u}+61 \end{align}$$
so:
$$\begin{align} 0&= v\\ 0&=8150-20000w\sin{u}\\ 0&=-135w+85\cos{u}+61 \end{align}$$
$$\begin{align} 0&= v\\ 8150&=20000w\sin{u}\\ 135w&=85\cos{u}+61 \end{align}$$
$$8150*135/20000=(85\cos{u}+61)\sin{u}\\$$
$$8150*135/20000=85/2\sin{2u}+61\sin{u}\\$$
this one last you need to solve for $u$ by some numerical method (I don't see a simple solution) and fill the number back to the second equation for isolated $w$. $v$ is obviously zero.
You can get the two solutions on wolframalpha.com
