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                 -                      (4.263)
                                             (ao)e = IXe + ,lYe + kZe                              (4.264)
Using the vector cross product rule,
                                       a x b x c = b(a . c) - c(b  a)                         (4.265)
We have
                 g2e X ?2e X Re = S2e(?2e . Re) - Re(?2e . S2e)                   (4.266)
                                                                =  (leg2e cos A  - rCe C2e siri } )(SZeRe siri A)
                                     - (-keRe  lr2~                                (4.267)
                                                         = ReS2~ COS } (le sin A + ke cos A)                       (4.268)
366              PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
The vector cross product
                    s2c X  Ve = ref2e Voy sin A - jc(S2c Voz cos A + Q,e Vox sin A)
                               + ke S2e Voy COS A.                                                                    (4.269)
Substituting and rearranging, we obtain the following equations ofmotionin Carte-
sian form:
                                  Re S2~ cos }.sin A + Xe + 2S2e Voy sin A = Fx.e                  (4.270)
                                                ye - 2(2e( Voz cos A +  Vox sin A)  =  Fy,                            (4.271)
                                              Re C2~ COS2 A. + Ze + 2<2e Voy COS A, = Fz.e                          (4.272)
　
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