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.