The aim of this project is to show the nonlinear dynamics of a vertically driven pendulum using Lego NXT. I use this toy in my Nonlinear Dynamics classroom.

Below you find building instructions and a video of the toy.

A pendulum with a fixed suspension point has two equilibria of which one is hanging downward and is stable, and the other one is standing upward and is unstable. The so-called vertically driven pendulum has a suspension point which moves sinusoidially up and down. The upward equilibrium position can become locally asymptotically stable for a certain exitation frequency.

The LEGO Vertically Driven Pendulum consists of a LEGO NXT microprocessor and a LEGO NXT motor which drives the suspension point up and down. A pendulum, being an axle of 6 studs, is connected can freely rotate around the suspension point. A LEGO NXT program reads the data of the built-in rotation sensor of the LEGO NXT motor and calculates it to an angular speed of the crank shaft (measured in RPM). The power which is delivered to the motor can be adjusted with the grey buttons on the LEGO NXT. The upward equilibrium is stable around 650 RPM.