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## Rigid body disk pendulum rotating on moving table

June 25, 2011   Compiled on November 11, 2018 at 8:40pm
Simulation of a pendulum made up of a small spinning rigid cylindrical bob in which the pendulum rod (assumed to have negligible mass) swings attached to a frame ﬁxed on top of a rotating table. The system has 3 degrees of freedom. The angle $$\theta$$ the pendulum swing angle. The angle $$\psi$$ the spin angle of the pendulum bob, and angle $$\phi$$ the rotation angle of the large table.

The angular momentum $$L$$ of the bob with reference to ﬁxed point in space as well as the bob absolute rate of angular momentum $$\frac{dL}{dt}$$ are calculated and displayed in vector form.

The instantaneous value of the system’s kinetic (red bar) and potential energy (blue bar) is illustrated graphically. Other options are available to help study this system in details.

The simulation was performed by ﬁnding the Lagrangian and constructing the 3 nonlinear equations of motion and solving them numerically using NDSolve.

The principal moments of inertia are used for the bob. The ﬁxed point in space that was used to calculate $$L$$ with respect to the point where the pendulum rod is attached to the frame.