Spring 2003 16.61AC1-4 The overall equations of motion are then ×U U 0R QU Fy R 0-P V F W U+QW-Rl V+ RU-PW w+Pt B T= H L TrP+l,R 0R Q Ixr 0 Ix2 P →M IvyQ+R 0-P 0|Q I2R+12P-QP012012R IP+lR +QR(I2z-Iuy)+ PQlzz IyyQ +PR(Irz-I22)+(R2-P)Ix2 I2 R+IrP +PQ(Iwy-Ixx)-QRIza Clearly these equations are very nonlinear and complicated, and we have not even said where f and T come from. Need to linearize!! Assume that the aircraft is flying in an equilibrium condition and we will linearize the equations about this nominal fight conditionSpring 2003 16.61 AC 1–4 • The overall equations of motion are then: 1 m F = ˙vc B + BIω × vc ⇒ 1 m      Fx Fy Fz      =      U˙ V˙ W˙      +      0 −R Q R 0 −P −Q P 0           U V W      =      U˙ + QW − RV V˙ + RU − PW W˙ + P V − QU      T = ˙ H B + BIω × H ⇒      L M N      =      IxxP˙ + IxzR˙ IyyQ˙ IzzR˙ + IxzP˙      +      0 −R Q R 0 −P −Q P 0           Ixx 0 Ixz 0 Iyy 0 Ixz 0 Izz           P Q R      =      IxxP˙ + IxzR˙ +QR(Izz − Iyy) + PQIxz IyyQ˙ +P R(Ixx − Izz)+(R2 − P2)Ixz IzzR˙ + IxzP˙ +P Q(Iyy − Ixx) − QRIxz      • Clearly these equations are very nonlinear and complicated, and we have not even said where F and T come from. =⇒ Need to linearize!! – Assume that the aircraft is flying in an equilibrium condition and we will linearize the equations about this nominal flight condition.