In the very first post of this thread Keith wrote...
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Also, you mentioned Jerk and Jounce ( sounds like
a b-list rap group ). I've also puzzled over the
physical meaning of these terms. It's rather like
trying to imagine higher dimensional shapes. One
dimension up is about all I can muster, which in
this case is Jerk. Standing on a carousel, with
the speed increasing and decreasing sinusoidally,
ought to do it. Perhaps a better term would be
"projectile vomiting" rather than jerk, huh??? (grin).
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..which got me wondering, as horselover_fats invariably does. ;-)
Let's concentrate on the length terms, velocity, acceleration,
rate of change of acceleration.
Now if one confines oneself to straight in-line motion, then
personally, I find it hard to think of the physical meaning
of acceleration, let alone rate of change of acceleration. Oh
I know that there is the push in the back one gets when taking
off in a jet - but this seems a very transitory affair, a bit
like the feeling of weightlessness they give trainee astronauts
by sending their plane on a parabolic trajectory.
Unlike velocity, which one can experience all day and all night,
one can only
experience in-line acceleration for brief periods.
However, there are ways of experiencing acceleration continuously.
The simplest way is to simply lie down on the floor. This will
give the push-in-the back acceleration of one G continuously.
Unfortunately, unless one can find some way of varying the mass
of the earth it is difficult to increase the value of acceleration
one experiences by prostration.
Though it is beyond modern technology to increase a billionaire's
lying-down-push-in-the-back acceleration sensation, it is within
the scope of modern technology to reduce it all the way down to zero,
and even reverse it so he experiences a lying-down-push-in-the-front
sensation.
One first constructs a long evacuated square section pipe contiguous
with the earths surface, load the billionaire thrill seeker into his
coffin which is fired down the coffin guide at an appropriate speed.
He will gradually feel the push in his back reducing and eventually
he will have a floating sensation and imagine he has risen ...upon
the clouds of heaven... to join the angels.
But as the coffin increases in speed he will feel himself crushed
remorselessly against the roof by the high tech monster version of
the wheel WSG refers to in his bab ballad.....
============================================
They branded me and broke me on a wheel,
And they left me in a hospital to heal;
And, upon my solemn word,
I have never, never heard
What those Tartars had determined to reveal.
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...and realise that far from entering heaven he is experiencing
hell on earth, for -
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et iterum dico vobis facilius est
camelum per foramen acus transire quam
divitem intrare in regnum caelorum
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So much for the second derivative, but what about the third?
How can we grasp what THAT means physically?
We know what the conservation law is. It is the conservation of
angular momentum, which makes up the trinity of engineering scale
conservation laws.
Conservation of momentum
Conservation of energy
Conservation of angular momentum.
At this point things start to get a bit complicated.
One can think of change of rate of acceleration as a ballet dancer
spinning with her arms outstretched and then by pulling her arms
in towards her body she can substantially increase her rate of spin.
However this view has the same objection as trying to understand
acceleration by confining oneself to straight in-line motion -
only in this case of course it is confining oneself to in-plane
motion. The dancer cannot manifest continuous change in angular
momentum. She can only manifest the difference between her arms
outstretched and her arms close to her body.
To manifest continuous angular acceleration one needs to play the
same trick as one played for manifesting continuous acceleration.
On has to subduct a velocity at right angles. Momentum involves a
velocity in the x direction, acceleration a subducted velocity in
the y direction so angular momentum will involve a second
subduction velocity in the z direction.
What does this mean in physical terms.
Well, get hold of a toy gyro. Trap both ends of the axis in a
horizonal circular slot which is held rigid. Spin the gyro. Then
force the gyro round the slot against its turning resistance. Two
forces will be operating - the force you are applying along the
slot, and the force one side of the slot is applying to the axis
end. If the slot is allowed to move in a vertical direction then
the two ends of the gyro will describe a double helix.
One can continue this process of subducting velocities at right
angles till the cows come home, thereby generating conservation
laws to our hearts content cos they are all manifestations of the
conservation of hierarchical velocities/momentums at different scales.
But "Hang on!" I hear someone complain,
"You have used up all three dimensions."
Mmm.....I have used up all three Cartesian dimensions which have
lengths which are unbounded toward the indefinitely large and the
indefinitely small. But the Cartesian geometry one is taught at
school is a mathematical abstraction. It can't be applied willy-
nilly to the real world. In the real world real things have upper
and lower bounds so one must use an x, y, and z geometry which
also has upper and lower bounds. This means that we can nest as
many spaces as we like in the manner of Russian dolls or Chinese
boxes [an appropriate model for me since I have both a Russian
and a Chinese daughter-in-law. 8-) ]
This is why, for example, there is no problem in mentally
visualising the "coiled-coiled-coiled-........coil." discussed in
http://www.escribe.com/science/vortex/m32032.html
Such a structure implicitly has upper and lower bounds at each
level since a coil cannot be smaller than twice the diameter of
the wire, nor larger than the coil one higher in the pecking order.
Cheers
Grimer
