Fa2004 16.3334-2 The basic dynamics are F=mi and th 1F=元+Bb× u. Transport thm m B T=互+B×H e Basic assumptions are 1. Earth is an inertial reference frame 2. A/ C is a rigid body 3. Body frame B fixed to the aircraft(i, j Instantaneous mapping of ie and Blw into the body frame: BW=Pi+Qj+Rk 1c=Ui+Vj+Wk B Uc)B R W By symmetry, we can show that Iru= luz =0, but value of Irz depends on specific frame selected. Instantaneous mapping of the angular momentum H=Hri+hui+hzk into the Body Frame given by H Ix0Ix21「P H h 0I2 yy 0 H 1x201� k) � � � Fall 2004 16.333 4–2 • The basic dynamics are: �˙ I � ˙ I F = mvc and T� = H 1 �˙ B F = vc + ω × �vc Transport Thm. BI ⇒ � m � ˙ B BI ⇒ T � � = H + ω × H� • Basic assumptions are: 1. Earth is an inertial reference frame 2. A/C is a rigid body 3. Body frame B fixed to the aircraft ( �i,�j, BI • Instantaneous mapping of �vc and ω� into the body frame: BIω� = P�i + Q�j + R� k �vc = U�i + V�j + W� k ⎡ ⎤ ⎡ ⎤ P U ⇒ BIω ⎦ B = ⎣ Q ⎦ ⇒ (vc)B = ⎣ V R W • By symmetry, we can show that Ixy = Iyz = 0, but value of Ixz depends on specific frame selected. Instantaneous mapping of the angular momentum H = Hx �i + Hy �j + Hz � k into the Body Frame given by ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ Hx Ixx 0 Ixz P HB = ⎣ Hy ⎦ = ⎣ 0 Iyy 0 ⎦ ⎣ Q ⎦ Hz Ixz 0 Izz R