I've been working through the math for landing leg shock absorbers. Given the worst-case situation that it must handle (initial contact velocity, maximum acceleration, and surface gravity), the program should determine the dimensions of the legs and the constants for the springs and damping. I'm midway through though so I don't have anything to show.
One thing's surprised me so far, if I've done the math right. If the shock absorber is a critically-damped spring, the deceleration is maximum at the moment of first contact and tails off rapidly thereafter. With an undamped spring the maximum deceleration occurs at the point of maximum compression; an underdamped shock absorber would presumably fall between these two extremes. It seems to me that the ideal landing gear would just decelerate at a constant rate, to maximize the amount of deceleration relative to the length of the shock absorber, but I don't know that any landing gear actually works that way.