Driven pendulum under construction

This applet simulates a driven pendulum. It is still in a very early stage of construction.

• The upper left panel shows the actual pendulum swinging.

• The lower left panel displays a Poincaré plot of the system. The points show the state of the pendulum at specific times. The horizontal value of the points are given by the angle f of the pendulum, whereas the vertical axis represents its angular velocity f'. Every time the driving external force vanishes, a point with the current coordinates (f,f') is plotted. One can distinguish ordered and chaotic behavior of the system by the patterns emerging.

• The parameters of the system are shown in the upper right panel. At the lower end of the panel the equation of motion of the pendulum is given. f'' is the acceleration of the angle of the pendulum. You can change the strength A and frequency B of the external force and the amount of friction C. The equations of motion are integrated in discrete time steps with value dt which can be changed. There are also buttons for erasing the Poincaré plot and for rescaling the vertical axis of the plot.

• NEW: You can choose to change the external force A with time by specifying the amount of change and the number of iterations after which the force is updated. You start and stop this feature by clicking on the GO (or STOP) button. The lower right panel then shows a plot where the horizontal axis is given by the value of A. Whenever the force changes sign (and a point is plotted in the Poincaré plot) a point is drawn with the value of the angle giving its vertical position. One can distinguish regions in A with ordered behavior where the plot shows a simple structure and again chaotic regions.

New features will be added with time.