Discussion
How many oscillatory modes does the classical stick-fixed longitudinal problem have?
Answer: C
The characteristic equation is a quartic, and for a conventional aeroplane it factors into two complex conjugate pairs, hence two oscillatory modes: the phugoid and the short period. One would leave two roots unaccounted for. Three or four oscillatory modes are impossible in a fourth-order system, since each oscillation consumes a conjugate pair and only two pairs are available. Unusual configurations can replace one pair with two real roots, giving fewer oscillations rather than more.
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