The spherical pendulum is similar to the Simple Pendulum, except that it moves in 3-dimensional space. This gives it an extra degree of freedom (2 in total) - the rotation about the z-axis, denoted by . The spherical pendulum is shown in the diagram below:

As with the Double Pendulum, we use Lagrange's equations again to help us derive the following equations of motion:
(Click Here to see the proof)

You can see the motion of this pendulum simulated in the applet below. Note that the ( x , y , z ) axes are displayed on the applet to make it more obvious as to how the pendulum is oriented, and that the y-axis is coming out of the screen.

If you can read this writing then either you do not have Java installed, or your Java is not new enough to view the applets on this site. You need Java 1.4 to view these applets.

As with the previous pendulums, in this applet you can adjust the initial values of , , , and of course l.

© Michael Hart 2004