Basketball Spinning on Finger:

The equations of motion used to simulate the system below was solved using a 3-1-3 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 ithere.

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.

Thin Disk Rolling on Table:

The equations of motion used to simulate the system below was solved using a 3-1-2 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.

Euler Angle Demonstration

A demo to help visualize euler angles and how the sequence order affects the final state.