= Cubic potential barrier phase portrait
{title2=$\dot x=v,\quad\dot v=6x(x-1)$}
For unit-mass motion in $V(x)=3x^2-2x^3$, the <mechanical energy> is $E=v^2/2+V(x)$. The origin is a <center equilibrium>, and $(1,0)$ is a <saddle equilibrium>. Energies $0<E<1$ have trapped periodic orbits around the origin as well as a separate escaping component to the right. The barrier energy has a <homoclinic orbit> returning to the saddle after a turn at $x=-1/2$, plus two saddle branches on $x>1$. Above the barrier, particles traverse the well and eventually escape to the right.
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