Why did the USSR fall?
schaffer at optonline.net
Mon Apr 23 17:58:42 MDT 2001
Mark Jones said:
> Soviet Russia had become by 1985 only one more link in the chain of
> world capitalism; when that link fell into the abyss it dragged the
> whole chain with it. There is a debate on this list about the
> differential calculus: perhaps one of the more numerate contributors
> can remind us of what happens when chains begin to slide off ledges.
well, since you asked ...
The upshot for the simplest possible model problem (no table/ledge
friction, uniformly sized links in chain): constant acceleration
downwards at 1/3 the acceleration of gravity. in other words, it is as
if the chain were in free fall on a planet with a third our gravity.
[ mark, re/ the big bang thread on the ole crashlist: there is a new
theory for the early universe floating around you'll be interested
in. i'll write about it another time. the authors of the theory call
it the "the ekpyrotic universe". but for you, i'd call it the
"crash-bang theory". its quite interesting.]
=== the rest is for the (very?) few physics buffs here and anyone else
that wants to be a bit more rigourous in the use of falling chain
models for Russia et al. ===
i have several friends who have worked on chain dynamics problems, one
of them worked with a company who made industrial chains and analysed
a similar class of problems.
turns out to be not so simple a problem. one needs a good physical
model for the links and how the links are chained together and what
happens when the "slack" in a chain gets taken up link by link. are
the links open and flexible, like chain for hanging stuff, or is the
junction fairly tight and constrained, like drive-chain or motorcycle
chain? also some interesting interactions with the edge of the table.
but all in all, once a link-chain (with all equal sized links) starts
to slide over the edge, its very difficult to stop since a.) all
"engaged" links share in the gain in kinetic energy obtained via a few
links falling through a gravitational potential (unless the chain is
all coiled up on the table) and b.) one more link over the side adds
equally to the gravity force pulling the rest of the chain and c.) the
edge of the table has little in the way of mechanisms by which it can
stop the slide. only external physics, for example, something external
to the system grabbing hold of the end lying on the table, or b.) some
condition forms at the edge of the table (as it wears away it forms
some kind of barb structure which accidentally grabs the chain and
stops its fall), or c.) something starts to catch the already falling
chains soon enought that friction between the table and the remaining
sliding chains causes the system to halt.
dynamics of chain is intimately related to how effectively impulsive
forces are transmitted across the links. there is also an initial
conditions problem: is the first link over the side bigger than the
rest so that the chain starts to slide? (assuming that for equal sized
links sliding does not get initiated). friction can't stop the runaway
in the sense that _if_ the initial "over the ledge" is enough to start
the ball rolling, err, the chain sliding, _then_ subsequent friction
can not stop it. again, thats in the case where all the links ar
engaged initially. if there is lots of slack in the chain to start, in
principle the tightening of the chain and the friction between chain
and table can stop the free fall when enough links are engaged and if
not too many links are alreay over the side.
there is a related problem which is chain falling onto a table, and
then one could build on this and study a chain falling from one table
top down to another at a lower level. there is interesting stuff there
-- for example, will some chain remain up at the top at the end of the
a good test for whether a "chain" is a good model for one's system is
to see if there is a gross asymmetry between push and pull. its easy
to pull on a chain, much harder to push on it.
by the way -- to end on a cultural note (ahem) -- (more) continuous
materials have a similarly interesting behavior. pour a little water
so it coagulates in a puddle (surface tension) near to the edge of a
table, and then take your finger and draw one edge of the puddle over
to the edge of the table and watch the puddle drain away rapidly.
similarly take some honey or ketchup or some kind of viscous fluid and
pour it from a height onto a table. the forces at the table and puddle
push back on the infalling stream in interesting ways, and under some
conditions you can see the honey coil around in a loop. i did it with
mustard from a squeeze tube at the barbeque last nite.
the startup dynamics of a long chain of boxcars at a rail stockyard
has similar interesting dynamics to the yanked -- but initially loose
tangents (weak links?):
seems to be a ton of papers on the web on supply-chain dynamics
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