Rigid body pendulum on a flywheel

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Rigid body pendulum on a flywheel

June 8, 2011 compiled on — Wednesday July 06, 2016 at 08:29 AM

This Demonstration simulates the motion of a rigid pendulum pivoted, with no friction, to a rotating flywheel. The pendulum is forced to spin on its axes by the flywheel's angular motion and at the same it can swing in a fixed 2D plane. The system has two degrees of freedom: $θ$ , which is the pendulum's swing angle, and $ϕ$ , which is the flywheel's rotation angle. The two nonlinear equations of motion are derived using the Lagrangian energy method.

The two equations are solved numerically and the motion is simulated. Interesting motion profiles can be observed by changing the system parameters and the initial conditions.