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In the linearised equations of motion, stability derivatives populate

  • A.The input matrix that determines the response to controls
  • B.The output matrix only
  • C.The initial condition vector
  • D.The system matrix that determines the modes

Answer: D

Stability derivatives sit in the system matrix, so they and the inertias fix the eigenvalues and hence the modes. Control derivatives populate the input matrix and decide how strongly a given control excites those modes. The output matrix simply selects which states are measured. The initial condition is the disturbance, which the derivatives act upon rather than form. Keeping the two matrices distinct is what makes it obvious why a bigger elevator changes response without changing the modes.

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