.
Figure 7-41.-Simple pendulum.
view B, and figure 7-40, view B, show platform
Pendulous oscillation is periodic angular
motion with the gravity vector as its midpoint.
operation with proper earth-rate and aircraft-rate
Periodic motion around the local vertical produces
torquing corrections.
obvious errors from an inertial platform.
An analog or a digital computer develops
This happens because misalignment about the
the signals necessary to properly torque the
horizontal plane introduces gravity components
gyros. The corrections for earth rate depend
on accelerometer inputs. The system will interpret
on the aircraft's position on the earth's surface.
gravity accelerations as horizontal acceleration of
The analog corrections come from highly accurate
the aircraft. The Schuler pendulum is a specially
potentiometers that produce trigonometric func-
constructed pendulum without the unwanted
tions of aircraft position. Position integrator
shafts drive the potentiometers. To maintain the
oscillatory motions of non-Schuler pendulums. It
is a special case of both the simple and the
stable element oriented to the north reference,
compound pendulums, which are discussed in the
torquing corrections rotate the platform. The
following paragraphs.
rotation is about the vertical axis compensating
for vehicle velocity.
SIMPLE PENDULUM. --The simple pen-
Schuler Pendulum
dulum consists of a small body suspended by a
weightless string. The motion of the simple
A pendulum is any suspended mass that is free
pendulum is both periodic and oscillatory. The
to rotate about at least one axis. However, its
center of gravity is NOT on the axis of rotation.
period of the simple pendulum is given by the
Therefore, any pivoted mass that is not perfectly
mathematical formula
balanced is, by definition, a pendulum. The
inertial platform is a pendulous device and,
therefore, behaves as all pendulums behave. It
aligns to the dynamic vertical when at rest. The
pivot axis and the center of gravity align with the
gravity vector. The center of gravity will be on
the bottom. Also, it tends to break into its natural
period of oscillation whenever the aircraft
accelerates.
