# Pendulum Hanging from Rolling Disk

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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.

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Contributed by: Erik Mahieu (April 2014)

Open content licensed under CC BY-NC-SA

## Snapshots

## 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:

,

.

## Permanent Citation