In order to explain the fundamental principle of operation of the PVRU 
in as simple a fashion as possible, consider a single axis of the system with 
motion in only one plane. The geometry of the situation is shown in Figure 1. 
We consider differentially small motions on the circle. Starting from point A 
with zero initial velocity, the distance ds is covered in going to point B. The 
distance to the point C would be given by the relation: 
Now note that the central angle, a, can be obtained from S by the simple 
equation: 
S = QR 
But in traveling from A to C the vertical changes in direction, relative to the 
fixed stars, by an angle 8 which is equal to @ . If, then, we had a platform 
which was stationary relative to the fixed stars (i.e. , gyroscopically stabil - 
ized) by rotating it through the angle 8=S/R as we moved, the platform would 
be kept in alignment with the local vertical. 
A first attempt in instrumenting this might be to provide an accelero- 
meter on the platform to measure the tangential accelerations of Figure 1. 
By performing a double integration on the output of this accelerometer, it would 
seem that the desired value of S would be obtained. A difficulty springs up when 
it is realized that no accelerometer can be built which would not also measure 
the acceleration of gravity. Thus, if the accelerometer were placed on the plat- 
form and the platform were not precisely vertical, a component of gravity would 
appear in its output. This leads us to alter the simple system just proposed. 
Also entering into the choice of the new system are considerations of a practical 
-8 =