On 3/8/2024 1:21 AM, Ross Finlayson wrote:

One thing I've been trying to figure out is
"the infinite higher-orders of acceleration".

This is where for example that classically
there's that "rest is rest and motion is motion",
and it's that v is dp/dt, rest 0 and motion non-zero,
it's meters/second, and in seconds/meter, it's
that motion is non-zero and rest is infinity.

So I'm wondering about v', v'', v''', that being
acceleration and its higher orders, out to v^prime-infty,
that at an instant, help figure this out.

For what it's worth, some higher derivatives have (somewhat whimsical)
names. The derivative of acceleration with respect to time is called
jerk, the derivative of jerk is called snap or jounce, the derivative of
snap is crackle, the derivative of crackle is pop. Someone was a
breakfast cereal fan. The highest derivative I know of that's actually
used is snap, when designing the transition of roads or railroads from
straight to a curve they try to minimize the 'snap' of a vehicle
following the transition segment.

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Volney wrote:

Ross wrote:

So I'm wondering about v', v'', v''', that being
acceleration and its higher orders, out to v^prime-infty,
that at an instant, help figure this out.

For what it's worth, some higher derivatives have (somewhat whimsical)
names. The derivative of acceleration with respect to time is called
jerk, the derivative of jerk is called snap or jounce, the derivative of
snap is crackle, the derivative of crackle is pop. Someone was a
breakfast cereal fan. The highest derivative I know of that's actually
used is snap, when designing the transition of roads or railroads from straight to a curve they try to minimize the 'snap' of a vehicle
following the transition segment.

I'd heard of jerk. Many years ago, Norman Dean "invented" the Dean drive,
a system of rotating masses with the center of rotation of the masses
being moved at particular times in the rotation cycle. He showed that the weight of the assembly was decreased when running - on a bathroom scales.

William O. Davis analyzed the system which was referred to by John W.
Campbell, Jr. as "the fourth law of motion" - i.e., jerk. Davis and G.
Harry Stine got together and tested the invention. They hung it from a
wire and oriented it so the supposed thrust would be horizontal. There
was no net thrust. The "weight loss" was due to nonlinearities in the
bathroom scales because of the thumping around of the weights.

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gharnagel <hitlong@yahoo.com> wrote:

Volney wrote:

Ross wrote:

So I'm wondering about v', v'', v''', that being
acceleration and its higher orders, out to v^prime-infty,
that at an instant, help figure this out.

For what it's worth, some higher derivatives have (somewhat whimsical) names. The derivative of acceleration with respect to time is called
jerk, the derivative of jerk is called snap or jounce, the derivative of snap is crackle, the derivative of crackle is pop. Someone was a
breakfast cereal fan. The highest derivative I know of that's actually
used is snap, when designing the transition of roads or railroads from straight to a curve they try to minimize the 'snap' of a vehicle
following the transition segment.

I'd heard of jerk. Many years ago, Norman Dean "invented" the Dean drive,
a system of rotating masses with the center of rotation of the masses
being moved at particular times in the rotation cycle. He showed that the weight of the assembly was decreased when running - on a bathroom scales.

William O. Davis analyzed the system which was referred to by John W. Campbell, Jr. as "the fourth law of motion" - i.e., jerk. Davis and G.
Harry Stine got together and tested the invention. They hung it from a
wire and oriented it so the supposed thrust would be horizontal. There
was no net thrust. The "weight loss" was due to nonlinearities in the bathroom scales because of the thumping around of the weights.

Yes, a mistake that is made over and over again.
There was some ado some time ago about some students
who had put a gyroscope on a precision 'balance'.
They noticed a change of weight that depended on the sense of rotation. Apparently the bearings are smoother in the direction
in which they are normally run,
producing less vibration to rectify,

Jan

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