Quote:
Originally Posted by sspoldi
Hillbilly solution:
one forward Euler integration, one backward Euler integration, less typing and good enough for government work.
Surprising how often that works...
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That is:
Code:
x'[n+1] = x'[n] + dt*x''[n] //backward looking
x[n+1] = x[n] + dt*x'[n+1] //forward looking
x''[n+1] = -x[n+1]
It looks OK on amplitude, but overpredicted the resonant frequency by .. almost half a part per thousand. Certainly good enough for FRC.
Quote:
Originally Posted by sspoldi
P.S. The equation (for the catapult) should be something like θ" = K1∙(K2 - θ'), θ is just along for the ride.
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The cosθ term is gravity acting on the boulder (and lever arm).