Modeling and Simulation of Self-Synchronizing Mechanical Systems

If certain conditions are met, mechanical systems can exhibit the remarkable ability to self-synchronize. This thesis implements low-order models of two such systems. The first models two coupled pendula attached to a rigid body—a system known as “Huygens’ clocks”. The two pendula are subject to excitation from an external moment applied by an escapement mechanism. There are two types of escapement models considered: Hamiltonian and Van der Pol. Depending on initial conditions and escapement parameters, the system will fall into one of three post-transient states, which are classified according to the phase difference between the two pendula. These states are in-phase synchronization, out-of-phase synchronization, and asynchronous motion. One objective of this thesis is to map parameter sets and initial conditions to one of these three states. The second model uses principles from the Huygens’ clocks model in an adaptation of the well-known “kicked rotor” system. The model consists of two kicked rotors that are coupled via their momenta. The responses of this system indicate rich dynamical behavior, including the possibility of synchronized chaotic motion.