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p i
p i
p i
p i +
p i
Figure 8.5.
Impulses at contact points (with friction).
Here μ can be negative, depending on the initial rope-slide direction; Fig-
ure 8.5 assumes that the rope slides from right to left. This yields
sin α
μ cos α
sin α + μ cos α .
P i
=P i
Thus, for each vertex we get the “outgoing” impulse from the “incoming”
one. Expressing P i and P i through P i and substituting the results into Equa-
tion (8.4), we get the vector impulse applied by each body to the corresponding
rope vertex (the impulse applied by the rope to each body will be its opposite):
P i
P i =(( d i− 1
d i )sin α +( d i− 1 + d i ) μ cos α )
sin α + μ cos α .
Now we can use the same approach as before, which is to apply a test impulse
to the contact sequence, measure the velocity response, and then do the same
during the solving with a real impulse (of course, the impulse will no longer stay
constant from vertex to vertex—it will be changed according to Equation (8.5)
after each one).
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