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George, you wrote:
"But I wonder whether he has got that right. The three directions he has
specified are not fixed in space, but rotate with the Earth. Three axes,
fixed in space could be- Toward the North celestial pole, with Dec = 90:
toward Aries (in the Earth's equatorial plane), with Dec = 0,
Right-Ascension = 0: and (also in that equatorial plane) 90 degrees from
Aries, with Dec = 0, R.A. = 90. These axes remain (nearly) unchanging, in
space."

Yes, thanks. I meant SHA and typed GHA. In a spacecraft (or in a fundamental
theoretical case), you want to keep fixed directions in inertial space, so
fixed SHA is what you're looking for. In practice, it's normal for
applications near the Earth's surface to rotate the platform at the sidereal
rate. In older systems based on real gyros mounted on a physical platform
mounted in gimbals, this was done with something like a telescope's clock
drive turning at the sidereal rate. In modern "strapdown" inertial systems,
the "platform" is virtual so the sidereal rate rotation is done in software.

And you wrote:
"FOG stands for fibre-optic gyro, and is technically somewhat different from
the other type, the ring laser gyro, but for our purposes we can consider
them to be effectively the same thing. All are extremely precise, and VERY
expensive."

Yeah, from my perspective, thinking purely in terms of the physics that
"makes them go", FOGs and RLGs are variations on a theme. They are "Sagnac
effect" devices. I have been told that FOGs are significantly less expensive
which is why people in the industry saw them as a major improvement over
RLGs when they began appearing about twenty years ago. The price of an
isolated component can be difficult to quantify, but does anyone in the
group have any real idea if this price difference is real?

You wrote:
"However, I suggest he has no call to apologise for doing so." [discussing
something outside the bounds of traditional navigation]

It was a pre-emptive strike. 

And you wrote:
"Although inertial navigation systems always show some drift, as a result of
having to integrate (twice) the accelerations, which always have some
zero-error, I doubt (from my inexpert perspective) whether any of that drift
derives from the pseudo-gyros, which sense the orientation. They are looking
at the position of interference-fringes of light, which shift as the device
rotates, but which ought to stay rock-solid, in the absence of any such
rotation in space."

But those darn photons are bosons. They "like" being in the same state, and
they tend to produce standing waves when the rotation rate is slow.
Apparently this is a bigger problem with RLGs than FOGs. RLGs in real
navigation systems are equipped with little vibrating devices to keep them
lively. These tend to prevent the counter-rotating beams from locking into
the same state.

And you wrote:
"However, if they are strapped-down to a platform that is horizontal to the
Earth's surface, then they will partake in the Earth's rotation, in a way
which depends on latitude, and if that platform moves about on the Earth,
the resulting shifts in the "horizontal" will also affect them."

Apart from the sidereal rate rotation that I mentioned above, there's a lot
of this that can handled when the system boots up. For example, in some
aircraft INS systems, they can calculate a fairly good latitude value and
true north direction by watching the rate of rotation of the vertical with
respect to directions in inertial space. The system "observes" the motion of
the vertical (maximum acceleration direction for a motionless vehicle) for
five minutes relative to the spatially fixed axes.

Most of my information is anecdotal so some of it may be rumor. I've never
touched an INS or seen one outside of a museum. I understand more than a
little about the theoretical aspects, but only "a little more than a
little". 

Here's a fun link regarding a home-built inertial navigation system:
http://www.tmoser.ch/typo3/11.0.html . The test results are interesting.
After one minute of motionless operation, their homebrew INS had an error in
the vertical of 5.0 degrees growing steadily and 40 meters in position
growing rapidly. These are related, of course. If your vertical is wrong,
then a horizontal accelerometer will think that some portion of the local
gravity acceleration is actually vehicle acceleration. A small error, theta,
in the vertical leads to some horizontal acceleration a=g*sin(theta) which
then grows as (1/2)*a*t^2. But I suspect these guys could have done better
with more sophisticated software. There are ways of taming these errors.

I'll close this message with a connection taking us back to the 19th
century. Here's a letter to the editor of "Nature" published in 1959
referencing another letter published way back in 1873:
"D. CHILTON
Department of Astronomy and Geophysics, Science Museum, London, S.W.7. Oct.
9.

THE recent voyage of the submarine Nautilus below the polar ice has caused
interest to be focused on the subject of 'inertial navigation'. This recalls
to mind a communication which was published in Nature (7, 483; 1873). A
correspondent, Joseph John Murphy of Co. Antrim, discounted the idea that
"the instinct of direction in animals is of the same kind as the faculty by
which men find their way" and suggested instead a mechanical analogy
basically identical with 'inertial navigation', namely: "If a ball is freely
suspended from the roof of a railway carriage it will receive a shock
sufficient to move it, when the carriage is set in motion: and the magnitude
and direction of the shock ... will depend on the magnitude and direction of
the force with which the carriage begins to move ... " " ... every change in
... the motion of the carriage ... will give a shock of corresponding
magnitude and direction to the ball. Now, it is conceivably quite possible,
though such delicacy of mechanism is not to be hoped for [my italics,
D. C.], that a machine should be constructed ... for registering the
magnitude and direction of all these shocks, with the time at which each
occurred ... from these data the position of the carriage ... might be
calculated at any moment." "

 -FER



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