The determination of the long-term behavior of periodic orbits is considered. Different numerical techniques, including the Lyapunov Exponent, the Smaller Alignment Index, and the Generalized Alignment Index are used. Because of the discontinuous nature of the system under consideration, these methods are found to be insufficient and a more simplistic approach is utilized. The simplistic approach determines long-term behavior up to 500 periods of an orbit. It is found that in-phase periodic modes result in the largest amount of stable modes. Future work will look at the common characteristics of the in-phase modes to better understand why they are more likely to be stable.
Johnson, Bo, "Determing the Chaotic Nature of Periodic Orbits" (2020). Physics Capstone Projects. Paper 81.