of Figure 4. It will be noted that since the inner, or vertical element of the 
system is fixed in azimuth relative to the stars, its orientation changes relative 
to the aircraft and consequently the roll and pitch axes of the platform. It is, 
therefore, necessary to resolve the control signals generated by the accelero- 
meters and integrators into the components required for roll and pitch of the 
platform. This is the most fundamental change in the system. There are, how- 
ever, less basic changes but ones which are sufficiently important to be briefly 
mentioned: 
A system of this sort was shown to have a period of oscillation of 84 min- 
utes. Examination of Equation (5) will show that this oscillation is undamped. 
It will, therefore, have an amplitude equal to the initial offset and the amplitude 
will remain unchanged with time. Such a system would be impractical to set 
up in initial alignment with vertical since the period is inconveniently long. Pro- 
vision is consequently made to shorten the period and to provide damping when 
the system is started on the ground. After the initial errors and the resulting 
transient oscillation has died away, the system is restored to correct "Schuler 
tuning." This is the purpose of the switched functions. 
All the previous theoretical analysis has been made on the basis of a 
spherical earth which is not rotating. These assumptions are, of course, not 
true. The rotation of the earth produces the same effect as the equivalent mo- 
tion of the platform vehicle. It has been shown that the platform aligns itself 
with the gravity vector regardless of its motions, the platform will therefore 
align itself so as to be perpendicular to a line to the gravity center of the earth. 
During initial set up, the platform must therefore be so oriented. At that time, 
- 8 —