A gyroscope is a rotating physical device that, due to the law of conservation of angular momentum, tends to keep its axis of rotation oriented in a fixed direction. A rigid body is a gyroscope if the inertia tensor relative to the barycenter admits a simple eigenvalue and a double eigenvalue or a triple eigenvalue. The eigenvector corresponding to the simple eigenvalue is called the gyroscopic axis.

A gyroscope is used for measuring or maintaining orientation and angular velocity; the gyroscope utilizes the angular momentum of a heavy spinning disk, called a rotor, to sense angular motion of its base about one or two axes at right angles to the spin axis. The rotor is mounted and moves within gimbals within a frame and maintains its orientation regardless of any movement of the base.

Gyroscope in function

At high speeds, the gyroscope exhibits extraordinary stability of balance and maintains the direction of the high speed rotation axis of its central rotor. The implication of the conservation of angular momentum is that the angular momentum of the rotor maintains not only its magnitude, but also its direction in space in the absence of external torque. The fact that it will stay upright as long as it is spinning fast enough demonstrates the property of gyroscopic inertia: the direction axis resists change. This means that a gyroscope mounted universally, in double gimbals, will maintain the same orientation in space however its support is turned, a property applied in many navigational devices.

Precession on a gyroscope
Precession on a gyroscope. Note that the angular momentum vector is pointing starting at the top point towards the fixed point (also applies to the gimbal).

The first known apparatus similar to a gyroscope (the “Whirling Speculum” or “Serson’s Speculum”) was invented by John Serson in 1743. It was used as a level, to locate the horizon in foggy or misty conditions. But, the first instrument used more like an actual gyroscope was made by Johann Bohnenberger of Germany, who first wrote about it in 1817. The classic type gyroscope finds application in gyro-compasses, but there are many more common examples of gyroscopic motion and stability. Spinning tops, the wheels of bicycles and motorcycles, the spin of the Earth in space, even the behavior of a boomerang are examples of gyroscopic motion.

Uses of the gyroscope

The operating principle of the gyroscope is exploited to build:

  • Gyro-compass, a device that can replace the magnetic compass (it indicates geographic north unlike the magnetic compass which indicates magnetic north).
  • The gyroscope is used on military ships to maintain the pointing of missile launchers towards a target and antennas towards a satellite, freeing the pointing from the rolling and pitching movements of the ship itself.
  • Artificial satellites, space probes and spacecraft, in particular is the basis of the inertial guidance system, which keeps the vehicle oriented with respect to fixed stars. In the Hubble Space Telescope, for example, it is used to keep the telescope pointed precisely toward the observation point.
  • Games such as the spinning top and the yo-yo.
  • Firearms, to impart a rotation in the motion of the projectiles, in fact the barrels of many firearms have an internal slightly helical rifling that imparts a rotation to the projectile that can give stability to the trajectory, keeping the projectile always aligned in the same direction.
  • Radio-controlled motorcycles, in radio-controlled model motorcycles, a gyroscope is used in the drive wheel in order to maintain balance.
  • In the United States, in the early 2000s, a small vehicle with two parallel wheels kept vertical thanks to a system of gyroscopes and feedback systems on the motors was invented, called segway HT.

Other types of gyroscopes

Alternatives to the traditional gyroscope are:

  • Optical, fiber optic or laser gyroscopes; in these, two beams of light are directed along two curved or polygonal paths on the perimeter of a figure perpendicular to the axis whose rotation is to be evidenced. They are based on the relativistic principle that the speed of light is constant in every inertial reference. If the described system undergoes a rotation around the axis, the two light rays will take different times to make the two paths, and an interferometer can detect this difference.
  • Systems using extremely sensitive piezoelectric crystals as sensors. Three of these sensors arranged parallel to the three Cartesian axes are capable of detecting minute changes in orientation. Compared to the traditional mechanical gyroscope these systems are much more sensitive and having no moving parts, faster in response.
  • Capacitor gyroscopes, use differential capacitors to encode capacitor displacement and Coriolis force so as to read angular acceleration into integrated electronic systems.