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’s pulley, except for the degrees of freedom of one of its two masses. Indeed it can swing in a bidimensional plane, producing a system that - for some values of parameters and initial conditions - turns out to be chaotic. This machine consists of two masses connected by an inextensible and massless rope, that can move on two radiusless and massless pulleys. Moreover the two masses can not collide. The study of the Swinging Atwood’s machine dynamics is made with Lagrangian mechanics. Numerical and graphical simulations of the chaotic system are made and the Lyapunov’s exponent is calculated for a thousand values of mass ratio.