Application
A pendulum the length of the Earth's radius is impractical, so Schuler tuning doesn't use physical pendulums. Instead, the electronic control system of the inertial navigation system is modified to make the platform behave as if it were attached to a pendulum. The inertial platform is mounted on gimbals, and an electronic control system keeps it pointed in a constant direction with respect to the three axes. As the vehicle moves, the gyroscopes detect changes in orientation, and a feedback loop applies signals to torquers to rotate the platform on its gimbals to keep it pointed along the axes.
To implement Schuler tuning, the feedback loop is modified to tilt the platform as the vehicle moves in the north-south and east-west directions, to keep the platform facing "down". To do this, the torquers that rotate the platform are fed a signal proportional to the vehicle's north-south and east-west velocity. The turning rate of the torquers is equal to the velocity divided by the radius of the Earth R:
So:
The acceleration a is a combination of the actual vehicle acceleration and the acceleration due to gravity acting on the tilting inertial platform. So this equation can be seen as a version of the equation for a simple gravity pendulum with a length equal to the radius of the Earth. The inertial platform acts as if it were attached to such a pendulum.
Schuler's time constant has other applications. Suppose a tunnel is dug from one end of the Earth to the other end straight through its center, a stone dropped in such a tunnel oscillates with Schuler's time constant. It can also be proved that the time is the same constant for a tunnel that is not through the center of Earth also.
Read more about this topic: Schuler Tuning
Famous quotes containing the word application:
“We will not be imposed upon by this vast application of forces. We believe that most things will have to be accomplished still by the application called Industry. We are rather pleased, after all, to consider the small private, but both constant and accumulated, force which stands behind every spade in the field. This it is that makes the valleys shine, and the deserts really bloom.”
—Henry David Thoreau (18171862)
“It would be disingenuous, however, not to point out that some things are considered as morally certain, that is, as having sufficient certainty for application to ordinary life, even though they may be uncertain in relation to the absolute power of God.”
—René Descartes (15961650)
“The application requisite to the duties of the office I hold [governor of Virginia] is so excessive, and the execution of them after all so imperfect, that I have determined to retire from it at the close of the present campaign.”
—Thomas Jefferson (17431826)