Text: Classical Mechanics by John Taylor

Chapter 7: Lagrange’s Equations

Coupled Pendulum
These pendulums are coupled by a spring, demonstrating complex modes of oscillation modeled by its Lagrangian. Showing students these different modes in action is a great way to grasp the physics and math behind this system.

Atwood Machine and Double Atwood Machine:
Both the single and double Atwood machines (like the coupled pendulum) are good demonstrations to use when discussing the Lagrangian.

Cycloid Ramp
A series of ramps demonstrating the fastest path between two points.

Chapter 10: Rotational Motion of Rigid Bodies

Motor-Driven Gyroscope
This demonstration is a good one to present during the lesson on rotational motion for rigid bodies. By adding and subtracting weight from the gyroscope you can see how the precession of the gyroscope will change.

Gyroscope to Demonstrate Precession and Nutation
This gyroscope demonstration shows not only precession, but will also show the different nutation patterns that occur when the gyroscope is pushed off balance.