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MAE142_Lecture11

MAE142_Lecture11 - Equations of Motion Force Equations...

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Equations of Motion Force Equations Moment Equations History Note MAE 142 NASA Image

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2 MAE 142 Body-Axis Forces and Moments rolling moment (L) pitching moment (M) yawing moment (N) z B y B x B longitudinal force (Fx) vertical force (Fz) side force (Fy)
3 MAE 142 Force Equations Use Newton's Law to develop the force equations in the body-fixed frame. a o B = ˙ v o B   v o B m a o B = F B m g B g B = T L2B g L m [ ˙ u ˙ v ˙ w ] m [ 0 r q r 0 p q p 0 ][ u v w ] = [ F x F y F z ] m [ g sin g sin cos g cos cos ] m ˙ u qw rv = F x m g sin m ˙ v ru pw = F y mg cos sin m ˙ w pv qu = F z m g cos cos

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MAE 142 Angular Momentum The moment equations start with an expression for angular momentum. h B = I B  B I B = [ I xx I xy I zx I xy I yy I yz I zx I yz I zz ]  B = [ p q r ] I xx = y 2 z 2 dm I xy = xy dm etc. etc.
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MAE142_Lecture11 - Equations of Motion Force Equations...

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