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AAE556 Lecture 33 Vg Method revisited

... 2  µ ω2   ω 1  + Lα  + a  − Lh  + a  µ 2  µ 2  Purdue Aeroelasticity Theodorsen’s method The system is self-equilibrating h  Fo A  ÷+ Bθ = =0 mb b ω Lh ω ω =− − + ω µ ω ω ATM...
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AAE556 lecture 23 Representing motion with complex numbers and arithmetic

... Using complex numbers and doing complex arithmetic provides advantages i We use one complex arithmetic equation instead of two real equations to find the amplitudes of the motion The equation of motion ... plunge and the twist motions are not “in phase.” 2) The Real part of the complex function gives us the expression for the actual motion Summary We have two different types of motion, pitch and ... necessary x(t ) = x1 cos ω t + x2 sin ω t Solution approach using complex numbers – put complexity into the problem with a single complex equation Response ( x( t ) = Re Xe To forcing iωt ) imaginary...
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