NOTES
Now for some details on errors - starting with Schulers. This chart shows a correctly aligned platform (one that “knows” the correct direction of the buoyant force). As the platform moves across the surface of the earth, the inertial navigator must calculate the new direction of gravity. The correct adjustment is that the rate of change of the direction of the buoyant force is velocity over the radius of the earth.
Now suppose that the alignment of the platform is incorrect by a small angle delta theta. The navigator's calculation of horizontal acceleration will be incorrect by -g*sin(delta theta), because its calculation of horizontal will be incorrect, leading to a miscalculation of horizontal velocity (even if the ship is not actually moving). Due to this error, the required adjustment to theta will be incorrect - leading to this equation for the change in the theta error. This equation describes an oscillator with a period of 84.4 minutes - the Schuler Period (not-coincidentally, the period of a satellite going around the Earth at ground-level).
The title of the talk is Chaos, Contingency and a Couple of Pendulums - the “Schuler “ pendulum is the other one.