Rotating frames, small oscillations about equilibrium, and the principle of least action behind it all.
Rotating Reference Frames: Centrifugal & Coriolis Rotating Liquid Surface Pivoted Rod on Car Truck Door Pendulum on Moving Pivot Weight on a Car's Wheels Gyroscope and Acceleration Spinning Top in an Elevator Apparent Force of Gravity: Equator vs. Poles Velocity in Plane Polar Coordinates Train on Tracks Apparent Gravity vs. Latitude Racing Hydrofoil Pendulum on Rotating Platform Oscillation of Bead with Gravitating Masses Oscillation of a Particle with Two Forces Normal Modes and Symmetry Pendulum Phase Portrait Bead on a Rotating Hoop Kapitza Pendulum Double Pendulum Chaos The Principle of Least Action Brachistochrone Race Noether's Theorem: Symmetry and Conservation