Can any one explain Schuler cycle in Inertial Navigation System

[gkraju]

Can anyone please explain schuler cycle, please don not start explaining with same old pendulum with the length of radius of Earth stuff.
why is it required ?
what is that all about ?

 

[JLFarrell]

Sketch a circle and draw radii to each of two positions, true (T) and estimated (E). Let the angle between the radii be exaggerated but still narrow enough to allow small-angle approximation (sine=angle in radians).
Since accelerometers sense the NONgravitational part of acceleration, we have to supply the gravitational part ourselves -- vectorially. So:
Calling the chord distance "x" the radius "r" and gravity "g" note that
* the true gravity vector is vertical (down along the radius
from "T")
* the apparent gravity vector (down along the radius from
"E") has a small projection along the chord from "T" to "E"
producing a horizontal error in acceleration, OPPOSITE the
direction of position error.

By the small-angle approximation and the opposite sign, the acceleration error is then
(-x/r) g = (-g/r) x
i.e., the second time derivative of "x" equals (-g/r) times "x" -- that's the differential equation of a sinusoid. Plug in numbers for Earth radius and gravity -- you'll get an amount in radian/sec corresponding to a period between 83 and 84 minutes.
There's a little more to it but that explains the basics. For more info I'll cite a tutorial at http://www.ion.org/tutorials/

<< additional book reference deleted by Mentor >>

 

[NatSusan]

The Schuler cycle is a phenomenon in which a gyroscope on a rotating Earth will maintain its orientation with respect to the fixed stars, rather than the rotating Earth. This is due to the fact that the Earth's rotation and gravity create a force that acts on the gyroscope in a way that counteracts the Earth's rotation.

This cycle is important because it allows for the accurate navigation of vehicles and airplanes. By using a gyroscope that is unaffected by the Earth's rotation, these vehicles can maintain a constant heading and avoid drifting off course.

The concept of the Schuler cycle is also used in the design of inertial guidance systems, which are used in missiles and spacecraft. These systems use gyroscopes to measure and maintain the orientation of the vehicle, even when it is moving through space.

In short, the Schuler cycle is a fundamental principle in navigation and guidance systems and is crucial for accurate and precise movement in a rotating reference frame.