The SHAKE Algorithm Applied to the Lattice Newton’s Cradle

This report summarizes an investigation of the use of the symplectic SHAKE integrator to simulate a generalization of Newton’s Cradle. A simple inverse-power repulsive potential is used to model the interactions of the pendulums. The main focus of the investigation is to explore the effectiveness of the SHAKE integrator and a continuous potential in the modeling of Newton’s Cradle. The solution obtained by numerical integration is compared with Newton’s Cradle using qualitative measures. Although a rather large power is needed in the repulsive potential to produce a realistic model, the SHAKE method is shown to be a relatively robust integrator in numerical experiments. Qualitative analysis of the numerical solution is provided by an interactive visualization interface written in OpenGL.