Kapitza's pendulum

Simulation of Kapitza's pendulum and a spring variant. The Kapitza pendulum is known for its stable inverted position.

The video demonstrates various regular and chaotic motion. The wheel is rotating with a constant angular velocity yielding a harmonic motion of the pendulum pivot. The energies of the systems are not constant due to their explicit time dependence, specifically the work done from the wheel. The simulation is still symplectic.

Kapitza pendulum details:
The system is a nonseparable and non-autonomous Hamiltonian system with one degree of freedom in addition to its explicit time dependence. The system was derived for any evolution of the pivot position (fpx(t),fpy(t))

Kapitza spring pendulum details:
The system is a separable and non-autonomous Hamiltonian system with two degrees of freedom in addition to its explicit time dependence. The dynamics of this system is similar to the regular Kapitza pendulum if the spring is sufficiently stiff.

The simulation was performed in real time using high order explicit integrators and video segments were rendered in real time.

🎵 "Z-TecH 1" by "Svenzzon" | CC | not affiliated with/endorsed by.

[uzha]

Algorithm wassup let this have a million views in 3, 2, 1...

[PendragonDaGreat]

The solid stick kinda looks like it's raving out in the stable inverted position.

Throw yours hands in the air like you just don't care.