sort, such as what sorts of accurate integrators are available. The bare bones 
of one axis of a system would be given by the Block Diagram of Figure 2. 
An accelerometer is shown mounted on a vertical platform. Its output 
is the tangential acceleration, a, plus a component of gravity. Suppose that 
the platform deviates from local vertical by a small angle © , the component 
of gravity measured by the accelerometer would be 8g . This net output of 
the accelerometer is then divided by R and integrated. The result of these op- 
erations is then: 
ä -f' 2-39 di 
o 
CHE : J 2 ar — 82 at 
At this point it is necessary to explain some of the detail of the instrumentation. 
Actually the next two blocks are physically realized by a single instrument, an 
integrating gyroscope. This instrument is a single degree of freedom gyro- 
Scope, restrained in the free axis by viscous friction. The free axis is also 
provided with a torquer. 
Now the output of the first integrator ( 8) is applied to the torquer in 
the free axis of the gyro. The gyro responds by rotating at a rate propor- 
tional to 0 The output angle is therefore equal to the integral of 6 
But there is also another cause of rotation. The gyro is mounted on the plat- 
form oriented to measure the platform rate. The rate establishes a torque in 
the free axis and the response to the torque (due to the viscous friction) is a 
rate. Thus the angle through which the gyro moves due to the platform motion 
is proportional to the integral of the platform rate. Then the output of the inte- 
grating gyroscope can be written as: 
c 
24 =