Particle in a Cubic Potential
This simulation shows a particle moving in a cubic potential \(U(x) = x - \frac{1}{3}x^3\). The left canvas shows the potential energy landscape with a bowling ball representing the particle position. The right canvas shows the phase space trajectory \((x, v)\).
Adjust the initial position, velocity, and damping constant to explore different behaviors. The phase trajectory is colored by speed: blue is slow, red is fast.
\( \textcolor{midnightblue}{\textbf{Equation of Motion:}} \) \( \textcolor{maroon}{\ddot{x} + c \dot{x} + (1 - x^2) = 0, \quad x(0) = x_0, \quad \dot{x}(0) = v_0} \)
\( \textcolor{midnightblue}{\textbf{Potential Function:}} \) \( \textcolor{maroon}{U(x) = x - \dfrac{1}{3}x^3} \)
Potential Energy Landscape
Phase Space Trajectory