A pendulum with oscillating attached point and a pendulum with the periodically changing length belongs to a class of physical systems called parametric. In the regime of small oscillations such systems are very well described through the Mathieu equations. In this work the equations of motion for these two parametric oscillators are numerically integrated without any restriction of small oscillations. Poincaré maps are obtained, showing that the chaotic and stable behavior can coexist for a given set of parameters which characterizes the system.
Parametric pendulum; computational simulation; chaos; Poincaré maps
