# How do I intuitively draw phase portrait from pseudopotential vs $x$ plot?

I am struggling with the process of deducing a phase portrait from pseudopotential vs $$x$$ plot. Is there a resource that would be helpful in understanding it better?

Given the pseudopotential(V) vs $$x$$ in the figure:

For different energy levels E(y= -4) = E1; E(y=0) = E2; E(y=4) = E3

I there a way to plot the phase portrait $$\dot{x}$$ vs $$x$$?

• the kinetic energy goes as velocity squared, so think about drawing the lines of equipotential for a 3d graph which is something like z = y^2 + x^3 – user1379857 Dec 12 '20 at 4:37
• More specifically, on a graph with axes $x$ and $\dot x$, graph $m \dot x^2 / 2 + k x^3 = const$ for different constants. – user1379857 Dec 12 '20 at 5:01