9860

Pendulum Hanging from Rolling Disk

A frictionless pendulum hangs from a disk rolling without slipping in a circular well. This Demonstration uses Lagrangian mechanics to compute the equations of motion of the disk and the pendulum and to plot the trace of the pendulum bob.
A horizontal energy gauge shows the total energy of the system, which remains constant while the potential energy and kinetic energy change in opposite directions. For higher energies, the motion becomes chaotic.

SNAPSHOTS

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

DETAILS

The circular well has radius . The disk with angular position has mass and radius . The pendulum rod with angular position has length and its bob has mass .
This is a system with two degrees of freedom: and .
The potential energy of the disk and pendulum system is .
The kinetic energy is .
The Lagrangian of this system is . Substituting this in the Euler–Lagrange equations for and ): , which results in the equations of motion:
,
.
    • 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.









 
RELATED RESOURCES
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 © 2014 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+