Environmental Engineering Reference
In-Depth Information
Axle
Cage
Flywheel
COM
Pivot
Figure 10.17
The parts of a simple gyroscope.
gravity. Instead of toppling over on the pivot when released, it precesses serenely
about the vertical direction. In more sophisticated incarnations, a gyroscope may
be mounted on a gimbal within a frame that allows it to take up any orientation to
the frame. In such a configuration the gyroscope's axle maintains its direction as
the frame tilts, and may be used to measure the orientation of the frame, a feature
that leads to applications in the navigation systems for aircraft and ships. We will
explore the simple gyroscope, treating it as an axially symmetric top, pivoted at its
base, and subject to a gravitational torque.
To gain a preliminary understanding of gyroscopic motion it is not necessary
to work in the body-fixed frame, so we will use the lab frame to start with, but
will switch to a rotating frame when we look at a more complex type of motion
called nutation. Furthermore, in the first instance only, we will make things easy for
ourselves by making the approximation that
lies parallel to the symmetry axis.
This is a good approximation as long as the flywheel rotates much more rapidly
on the axle than the whole gyroscope precesses about the vertical direction. In this
case, almost all of the angular momentum of the gyroscope comes from the rotation
of the flywheel about the axle. Figure 10.18 shows the gyroscope at an angle
θ
to
ω
e
3
q
m
g
R
O
Figure 10.18
A gyroscope at angle
θ
to the vertical.
