Active Trajectory
Particle
Background Flows
Min: -0.25 (Centers), 0.0 (Saddle)
System Equations:
Potential: $V(x) = -\frac{1}{2}x^2 + \frac{1}{4}x^4$
Energy: $E = \frac{1}{2}y^2 + V(x)$
Dynamics: $\dot{x} = y$, $\dot{y} = x - x^3$
Potential: $V(x) = -\frac{1}{2}x^2 + \frac{1}{4}x^4$
Energy: $E = \frac{1}{2}y^2 + V(x)$
Dynamics: $\dot{x} = y$, $\dot{y} = x - x^3$
Physics Note:
Notice how the particle oscillates within one well when $E < 0$, follows the homoclinic orbit (figure-8) at $E \approx 0$, and encircles both wells when $E > 0$.
Notice how the particle oscillates within one well when $E < 0$, follows the homoclinic orbit (figure-8) at $E \approx 0$, and encircles both wells when $E > 0$.