Tracking the spread of chaos in the swinging Atwood machine

Chaos is investigated in the swinging Atwood machine as the mass ratio μ decreases from the integrable motion at μ=3 to mostly chaotic dynamics at μ=2.7. The spread of chaos is characterized by combining a stability index with a Poincaré surface of section. An effective computational solution requires a consideration of numerical overflow issues. Once these are resolved, the computation shows that the spread of chaos, in this parameter regime, is associated with a hyperbolic periodic loop orbit. The example illustrates how to incorporate computational physics—such as the regularization of a singularity—into the undergraduate curriculum.