# Gyroscopes

The angular momentum of a spinning mass makes that mass's spin axis tend to maintain its orientation in inertial space unless torque is applied normal to the spin axis.   This property is used in various ways by devices that are called "gyroscopes" ("gyros" for short). Gyros in missiles are primarily of two types: 1) the two-degree of freedom gyro (2DOF gyro or "free" gyro), and 2) the rate gyro.

Free (2DOF) Gyro

If two ideal free gyros could be built - gyros without friction, mass imbalance, or other imperfection - they could tell us how a body, to which they are mounted, is oriented with respect to some "absolute" non-rotating frame of reference (i.e., an inertial frame). To tell us this, the gyros must be mounted on the body so that their spin axes are not parallel. The two spin axes then define a fixed plane in an inertial frame. It is especially remarkable that there is such a thing as an inertial frame and that the free gyro "knows" something about this frame!

The primary use of free gyros in a guided missile is to measure the missile's orientation in an inertial frame. Each free gyro can be instrumented to measure as many as two angles: the second and third angles in an Euler-angle sequence.  The particular Euler-angle sequence is defined by how the free gyro is mounted to the missile body.  A free gyro cannot measure the first angle in the sequence, because that angle must be turned about the gyro's spin axis. A corollary of this limitation is that, no matter how many free gyros you mount to the missile body, and no matter how you mount them, none of them can measure the first angle in any Euler-angle sequence. Sad but true. However, the Euler-angle measurements from two or more free gyros, properly mounted, can be manipulated mathematically to determine all three Euler angles and, hence, the missile's orientation in the inertial frame.

In many applications only the outer gimbals of the free gyros are instrumented.  In these cases each gyro provides a measurement only of the third angle in the Euler-angle sequence defined by the gyro's mounting.  Three free gyros are required in this case, each mounted to define a different Euler-angle sequence from the other two (
in this configuration, the spin axes of two of the free gyros can be parallel, but the inner and outer gimbals of one of these gyros must be orthogonal to the other gyro's respective gimbals).  The three measurements from the gyros are manipulated mathematically to determine the missile orientation.

Rate Gyro

By application of appropriate torque to its spinning mass, the gyro can be configured to measure the component of the missile's inertial angular rate about an axis defined by the gyro's mounting.  Descriptions of the various ways to configure the gyro for this function are beyond the scope of this short treatise.  Usually three rate gyros are mounted orthogonally to the missile body so that all three components of the missile's inertial angular rate can be measured.  These measurements are most often used by the missile autopilot to stabilize missile attitude.  If the measurements are very accurate, they can also be used by the missile's strap-down inertial navigation system (if there is one).