TRAJECTORY SOLUTION Treatises
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).