Aircraft Stability and Control by A. W. Babister

By A. W. Babister

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46a) 3 and I As a direct rotation that V"2 + + consequence Φ about a fixed l n3"3 of the fact Η i b3' ί 2 ' are constants coincident 4 6 b ) (during a w i t h η . , we see A c c o r d i n g t o E q . 2 . 1 5 , we have ' η3' Λ . =% . = a . 48) 2 "3 Careful and i^. 2 Pnlj l b u t s i n c eι, that i) and b. a r e " i n i t i a l l y " & · Ξ «,^. Ξ iu , f o r i = 1,2,3. Sl ( 3 of Eq. 5 [C] has EULER'S PRINCIPAL ROTATION THEOREM an eigenvector cosine eigenvalue of [C]. matrices imbedded in a rigid corresponding for t h e case Since rotation do i n f a c t 3) proves to a fixed line, if that (to within "proper" of unit direction right-handed axes of + 1 ; the eigenvalue a sign The l a c k of on ι and Φ ) e x c e p t sign uniqueness, as difficulty.

Not a be angles g i v e n r i s e t o many e l e g a n t m o t i o n a n a l o g i e s , the can the has h i s t o r i c a l l y terms pure using Problem") most energy oscillatory solution, the largest of motion periodic". 4 Rotational Equations o f Motion f o r R i g i d 55 Spacecraft l»(t)l = [ R ( e " ' ) ] I R ( 8 " ) J [ R ( e ' ) ] -8 -S 0 B 8 i -β 1 8_ Si -83 2 3 B 3 0 -83- 2 ~βο Bo &ι Q " 1 β COS ^ ρτ \ cos δ s i n i Ξ cos / ρ ( ,| { 0 l τ COS ^ \ Λ )-sin = υ \ \ I 0 \ - s i n δ sin ^ ρτ / \ 0 / ο c..

Observe t h a t Β C f o l l o w s f r o m d i f f e r e n t i a t i o n o f E q . 3 . 4) Β where we have control ignored volume substitution over the possible which the c space variation of integration o f E q . 3 . 1 , E q . 3 . 4 r e d u c e s t o t h e super more commonly " t h e t r a n s l a t i o n a l mR time the Η boundary of performed. 5) where F Ξ JJ7 d F , t h e v e c t o r sum o f a l l external Β J7J* d f = 0, for internal forces occurring f o r c e s a c t i n g on Β i n equal and o p p o s i t e pairs.

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