The Upward-Driven Disk, a Steadily Forced Chaotic Pendulum

TL;DR

This paper introduces a LEGO-based mechanical device called the upward-driven disk, which demonstrates chaotic behavior and mimics complex systems like fluid convection through steady upward forcing and oscillation.

Contribution

It presents a novel, easily constructed physical analog for chaotic systems, illustrating complex dynamics with a simple, visualizable LEGO device.

Findings

The disk exhibits steady, periodic, and chaotic motions.

The device mimics the Lorenz equations and fluid convection phenomena.

It provides an accessible platform for studying chaos in physical systems.

Abstract

An "upward-driven disk" is a novel mechanical device built from LEGO parts. A circular disk is suspended from the point where it is sandwiched between two wheels, making it free to oscillate as a pendulum, but the location of that suspension point on the disk changes with time due to a steady upward driving force applied by rotation of one of the wheels. The pendulum can dynamically flip between hanging downward and being inverted. Depending on the upward drive and the initial conditions, the disk can exhibit steady rotation, periodic motion, or chaotic motion (and some of these for the same drive). This device serves as an easy-to-visualize analog of chaotic phenomena in other physical systems. Most notably, the upward driven disk mimics a simplified version of the celebrated Lorenz equations that are frequently used to describe fluid convection.