Project
Swinging Atwood's machine
Numerical and graphical simulation of the chaotic system with computation of the Lyapunov exponent.
This project was conceived in the context of an honour program (PAF) at the Department of Physics of the University of Trento during the fall semester of 2018. It has later been modified, corrected and translated.
The Swinging Atwood's machine is a system similar to the Atwood pulley, except for the degrees of freedom of one of its two masses. It can swing in a two-dimensional plane, producing a system that — for some values of parameters and initial conditions — turns out to be chaotic. The machine consists of two masses connected by an inextensible and massless rope that can move on two radiusless and massless pulleys, and the two masses cannot collide.
The study of the dynamics is made with Lagrangian mechanics. Numerical and graphical simulations of the chaotic system are produced and the Lyapunov exponent is calculated for a thousand values of the mass ratio.