Home▸Chaos & Dynamics▸Kapitza Pendulum: Balancing a Rod Upside Down by Shaking the Pivot

🎯 Kapitza Pendulum: Balancing a Rod Upside Down by Shaking the Pivot

A rod that normally falls stands upright when its pivot is shaken fast enough. Explore the Kapitza pendulum: effective potential, the a²ω² > 2gl stability threshold, Floquet and Mathieu checks, and the chaotic tumbling below it.

Chaos & Dynamics3DAdvanced60 FPS📱 Mobile-adapted🟠 Blender

⚙ Under the hood

A rod that normally falls stands upright when its pivot is shaken fast enough. Explore the Kapitza pendulum, its effective potential and the a²ω² > 2gl threshold, checked against a Floquet matrix and the Mathieu series, with chaotic tumbling below it.

Kapitza PendulumChaosMathieu EquationEffective PotentialThree.jsBlender

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install