free body diagram Translational mechanical systems

In Static mechanics what is the meaning of the "principle of moments"   Need a detailed reponse!

It has been shown (Pounds, 2011) that an unloaded UAV helicopter is closed-loop stable and will have a characteristic equation given by S³ + $3 (m³h (92 + kka) + 918) s² I (kki+q₁) = 0 +k mgh I -S + mgh I where m is the mass of the helicopter, g is the gravitational constant, I is the rotational inertia of the helicopter, h is the height of the rotor plane above the center of gravity, 91 and q2 are stabilizer flapping parameters, k, kį, and ka are controller parameters; all constants > 0. The UAV is supposed to pick up a payload; when this occurs, the mass, height, and inertia change to m', h', and I', respec- tively, all still > 0. Show that the helicopter will remain stable as long as m'gh' I' 9₁+kki - 91gk k(q2 + kka)

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