Damped Spherical Pendulum

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 .


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+