I tried your proposed modification, but found that at the end of an
incremental move it causes the acceleration value to "ring" at the end
of the move.  The ring appears to be undampened and persists at least a
minute after the move ended.

I modified axis.ini to specify an acceleration of 2.0 (rather than 20.0)
for the X axis, then performed incremental jogs of 0.1 inch.

Screenshots of halscope
   http://emergent.unpy.net/files/sandbox/scope-old.png
        -- before the proposed change
   http://emergent.unpy.net/files/sandbox/scope-proposed.png
        -- after the proposed change
   http://emergent.unpy.net/files/sandbox/scope-proposed2.png
        -- zoomed in on the start of the ringing portion
           note change in scale of position (1u/div) and velocity
           (2m/div)

After the single incremental jog, emc won't start a new jog either.

So while I can't respond to the math, the empirical testing shows that
the current formula gives good behavior and the proposed one does not.

Jeff

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