This Demonstration traces the path of the bob on a damped spherical pendulum. The pendulum is suspended at the center of an imaginary sphere that marks the outer bounds of the center of the bob.

The equations of motion are

,

,

where and are the spherical coordinates of the center of gravity of the bob. The pendulum rod has length (with no loss of generality) and bob mass . The damping coefficient of the system is . The initial angular positions are and and the initial angular speeds are and .

Choose a set of parameters with the sliders or click the "randomize" button and start the animation. Run the animation to the end and press the "randomize parameters" button to discover a variety of bob trajectories.

A damping term is added to the equations of motion for the spherical pendulum programmed by Franz Brandhofer.

See also: A. Ertas and S. Garca, "Experimental Investigation of Dynamics and Bifurcations of an Impacting Spherical Pendulum," Experimental Mechanics, 49(5), 2009 pp. 653–662.