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2nd order short period dynamic mode approximation
in short period approximations, we assumed one degree of freedom (pitch rotation), but a real aircraft is rotating and translating in 6 total degrees of freedom. we need a static reference frame to describe these motions - most commonly a catersian earth coordinate system


lomgitudinal equations of motion
assumptions
L normal to V
drag parrallel and opposite to V
thrust acts along V
summing all forces around CG

complex planes (eigen values)

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