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
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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:
,
.
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