Mechanical gyroscope
Realizes: time-integral of angular velocity (orientation tracking)
A spinning rotor mounted in gimbals conserves angular momentum. Any external torque causes precession perpendicular to both the spin axis and the applied torque — rather than tilting directly. By reading gimbal angles, the device outputs the accumulated rotation of the platform relative to inertial space. It is a physical integrator: angular velocity in → angle out, with no arithmetic required. Inertial navigation systems chain three orthogonal gyroscopes with three accelerometers; double-integrating the accelerometer outputs (in the gyroscope-maintained inertial frame) gives position. Mechanical gyros guided Apollo missions and ICBM warheads; they have largely been replaced by MEMS and ring-laser gyroscopes but remain the conceptual anchor of inertial navigation. Speed: continuous real-time (spin-up time seconds to minutes). Capacity: 3-axis orientation; drift accumulates over time (arcseconds per hour in precision instruments).
Examples
Inertial navigation system — Wikipedia
An Introduction to Inertial Navigation — University of Cambridge
Technical primer on how gyroscopes integrate angular velocity and how accelerometers integrate to position in an INS