A Collection of Some Real Time Simulations I Made for Visualizing Dynamical Systems
CU Dynamics and Control Lab
December 2023

The equations of motion used to simulate the system below was solved using a 313 euler angle sequence. In the order of $\phi$, $\theta$, $\psi$. For more details on how this particular system was solved, you can find the article I wrote about it here
Feel free to orbit and zoom around with your mouse or finger, and use the sliders to mess around with the initial conditions. This simulation gives you a feel for how the various angular velocities affect the nutation of a symmetrical spinning top.
The equations of motion used to simulate the system below was solved using a 312 Euler angle sequence. In the order of $\psi$, $\theta$, $\phi$.
If you set $\dot{\psi_0}$ fast enough and decrease $\theta_0$ and $\dot{\phi_0}$ to something small, you can experience the coin enter a stable spin.
This simulation demonstrates the Intermediate axis theorem. Where if an object has three unique principal moments of inertia I1 > I2 > I3, the object will experience an unstable spin about the intermediate I2 axis.
If you set $\psi_0$ to 180$^\circ$, the tennis racket will experience an unstable spin.
A demo to help visualize euler angles and how the sequence order affects the final state.
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