Fa2004 16.3337-1 Aircraft Lateral dynamics Using a procedure similar to the longitudinal case, we can develop the equations of motion for the lateral dynamics Ax+ Bu T d yb= rsec go m g cos o 4=(+M)(+层N)(+层N)0 (ILLr+ tan e ere xxZ xxz I=Iax/(xI-盈) and 0 B 0� � � � Fall 2004 16.333 7–1 Aircraft Lateral Dynamics • Using a procedure similar to the longitudinal case, we can develop the equations of motion for the lateral dynamics ⎤⎡ v ⎥ ⎥ ⎥ ⎦ δa , u = δr x˙ = Ax + Bu , x = ⎢ ⎢ ⎢ ⎣ p r φ and ψ˙ = r sec θ0 ⎡ ⎤ A = ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ Yv Yp Yr m m m − U0 g cos θ0 ( I L � v + I� Nv) ( Lp + I� Np) (Lr + I� Nr) 0 zx zx I� zx I� xx xx xx (I� Lv + Nv ) (I� Lp + Np ) (I� Lr + Nr ) 0 zx I� zx zx I� I� zz zz zz 0 1 tan θ0 0 where I� = (IxxIzz − I2 xx zx)/Izz I� = (IxxIzz − I2 zz zx)/Ixx I� = Izx/(IxxIzz − I2 zx zx) and ⎡ ⎤ ⎢ ⎢ ⎢ ⎣ (m) −1 0 0 0 (I� xx) −1 I� zx ⎥ ⎥ ⎥ ⎦ ⎡ ⎤ Yδa Yδr ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ B = ⎣ L ⎦ δa Lδr zz) −1 · zx 0 I (I Nδa Nδr 0 0 0