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The missile updating code:
local dx=target.x-missile.x
local dy=target.y-missile.y
local accelx=missile.spring*dx-missile.damping*missile.vx
local accely=missile.spring*dy-missile.damping*missile.vy
missile.vx=missile.vx+ dt*accelx
missile.vy=missile.vy + dt*accely
missile.x=missile.x+dt*missile.vx
missile.y=missile.y+dt*missile.vy
It's pretty much just as written in his initial post, without normalization of (dx,dy) and without an external speed variable. You do have to play with the spring and damping constants quite a bit to get something that feels right.