numerical solution of differential equations

[GeeTwo]

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...

That is:

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.

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.

The cosθ term is gravity acting on the boulder (and lever arm).