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Cost cutting in procedurally specified simulations

Posted 10 years ago
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POSTED BY: David Gathercole
3 Replies

enter image description here - another post of yours has been selected for the Staff Picks group, congratulations !

We are happy to see you at the tops of the "Featured Contributor" board. Thank you for your wonderful contributions, and please keep them coming!

POSTED BY: EDITORIAL BOARD

Nice post, David! Do you have a force diagram and general form of equations you are solving?

POSTED BY: Sam Carrettie

A force diagram (tension excluded) can be shown nicely for the grass example, as the dynamic forces are defined directly from equations of angular derivatives, and thus have already been calculated. This also helps stress how easy it is to play with said forces, as they are stuck in after all the hard work.

grass forces

Arrows representing forces. Gravity, drag, and angular restorative forces are respectively blue, green, and red. Length proportional to square root of force magnitude.

The general equations would be as follows. All angle specified forces were appended, rather than worked with throughout (though you've incurred some self doubt here, I'll try to explicitly verify some assumptions soon.)

D[ MassOneX[t] ,{t,2}] = Sin[ AngleOne[t] ] TensionOne[t] + Sin[ AngleOne[t] ] TensionTwo[t]
D[ MassOneY[t] ,{t,2}] = Cos[ AngleOne[t] ] TensionOne[t] + Cos[ AngleOne[t] ] TensionTwo[t] + m g
...
D[ MassN-1X[t] ,{t,2}] = Sin[ AngleN-1[t] ] TensionN-1[t] + Sin[ AngleN-1[t] ] TensionN[t]
D[ MassN-1Y[t] ,{t,2}] = Cos[ AngleN-1[t] ] TensionN-1[t] + Cos[ AngleN-1[t] ] TensionN[t] + m g
D[ MassNX[t] ,{t,2}] = Sin[ AngleN[t] ] TensionN[t]
D[ MassNY[t] ,{t,2}] = Cos[ AngleN[t] ] TensionN[t] + m g
POSTED BY: David Gathercole
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