Real-time demonstration of the main characteristics of chaos in the motion of a real double pendulum

Abstract

Several studies came to the conclusion that chaotic phenomena are worth including in high school and undergraduate education. The double pendulum is one of the simplest systems that is chaotic; therefore, numerical simulations and theoretical studies of it have been given large publicity, and thanks to its spectacular motion, it has become one of the most famous demonstration tools of chaos, either through simulations or in real experiments. Although several attempts have been made to use the experiment in laboratory exercises, as the friction in the real experiment changes the nature of the motion and the values of characteristic parameters during the motion, examining the measured (dissipative) motion and comparing it with theoretical results raises several questions. In our review, we present a measurement system which is able to analyse these questions. The system, which consists of simple yet precise data acquisition electronics, easily attainable sensors, a Bluetooth module (to communicate with the PC) and open-source software, demonstrates on-line the main characteristics of chaos and the methods of its study and allows us to analyse the dissipative motion. Further information (including downloadable software) is provided on a dedicated page, http://www.inf.u-szeged.hu/noise/Research/DoublePendulum/.