A Simulation of a Charged Pendulum in Electric and Magnetic Fields

Mark Wellons

2008

For this independent study we constructed a simulation of a damped, charged, spherical pendulum in time-varying electric and magnetic fields and studied the pendulum's long term behavior. By analyzing a large number of oscillating electric field amplitudes and a number of constant magnetic field strengths, sets of system parameters that force aperiodic behavior in the pendulum were mapped. We find that as the electric field amplitude increases, the pendulum's long term behavior moves through periods of periodicity and aperiodicity. In addition, the qualitative effect of the magnetic field on the pendulum's periodicity is demonstrated. We find that the magnetic field narrows the windows of aperiodicity, and this effect increases as the magnetic strength increases. Each set of system parameters is independent of the others, so computation is parallelized using an Xgrid cluster. Further anaylsis of the pendulum's aperiodic behavior could rigorously show the sytem to be chaotic.