Pendulum Towing a Rolling Disk
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This Demonstration simulates the motion of a double pendulum with a rolling disk attached to the end of its lower rod. The disk is free to roll without friction over a horizontal plane.
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Contributed by: Erik Mahieu (October 2014)
Open content licensed under CC BY-NC-SA
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The pendulum's upper and lower rods have lengths and and angular positions and . The upper bob has mass . The disk has angular position , mass , and radius .
This system has only one degree of freedom: . The other variables are fixed by the algebraic constraints:
,
.
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 gives
,
,
which results in the equation of motion:
,
where and .
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