Wolfram Demonstrations Project

12,000+ Open Interactive Demonstrations
Powered by Notebook Technology »

Damped Spherical Pendulum

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.

[more]

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 .

[less]

Contributed by: Erik Mahieu (February 2010)
Open content licensed under CC BY-NC-SA

Snapshots

Details

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.

Embed Code

Take advantage of the Wolfram Notebook Emebedder for the recommended user experience.

Related Demonstrations More by Author
Browse all topics
Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send