I have discovered a method of completely characterizing the 6x6 response of all six types (x-,y-, and z- translational/rotational) of oscillatory disturbances at the base of the stack.

• "Tipping" drives are trivial, and simply require a face load in the appropriate direction.
• "Tilting" drives could use a torque, but I am instead implementing multiple edge loads in opposing directions to create the appropriate net curl. This curl will be kept constant across the three axes for sake of comparing the resulting transfer functions.
• "Tipping" responses are once again trivial, and merely require the displacement vector of the top center coordinate to be recorded.
• "Tilting" responses require the normal vector to be recorded and manipulated to produce the angular coordinates (assuming right-handed coordinate system):
  • θ_x = tan^-1(x/z)
  • θ_y = tan^-1(y/z)
  • θ_z = tan^-1(y/x)
    

The first three concepts have been confirmed through simulations to produce correct transfer functions. The last test seems to be producing some problems, in that the vector normal to the equilibrium position (an obvious and useless piece of information) is sometimes given instead of the vector normal to the position of maximum displacement. This means that, as of now, I have the capability of measure the half of the complete 6x6 matrix of transfer functions in the coming weeks. The first three of eighteen transfer functions are attached below and will be included in my progress report.