In general this problem would be insoluble, since there is no difference
in the nature of the acceleration of gravity and that due to centrifugal
force. A way out is offered, however, by the fact that true gravity acts
continuously and at a small angle to the axis of the gyro, while the
components which cause the pseudo-gravity are of short duration, liable
to rapid changes of direction, and, on a turn, act at a large angle.
What we require, therefore, is an erector which will respond slowly but
surely to the _average_ acceleration, which is downward, but too
sluggishly to be affected by the shorter period accelerations due to
turns or rolls. Slowness of response is a matter of the erecting forces
being small and of the mass and angular velocity of the gyro disc being
large. The success of the compromise called for depends on the relative
times taken for the gyroscope to tilt seriously from the true vertical,
due to the causes above mentioned, and for the average turn or roll.
Fortunately the former is a matter of minutes, the latter of seconds or
at the worst of fractions of a minute. More than this, since the roll or
turn is apt to be of much greater angle than any normal deviation of the
gyroscopic axis from the vertical in the same time, we are offered the
possibility of some device for filtering out the deviations which alone
are to effect the erector. For instance, by shunting the restoring force
whenever it is called upon to act through more than a predetermined
small angle.
As to the method of erecting the gyroscope, its characteristic property
must be kept in mind. This is that the axis does not tilt under an
applied force in the direction it would if the gyro were not rotating,
but around an axis at right angles to that of the applied couple. Thus
in Fig. 79, if a weight is attached as shown, the disc does not incline
downward toward the weight, around the axis _Y_, _Y´_, but _precesses_
about the vertical axis Z, Z´. Some means is therefore needed to
translate the pull which any gravitational control, such as a freely
swinging pendulum, would give, into a pull with _at least a component_
at a finite angle to this.
Public-domain text, read in full here on John Shaqi.
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