CONNECTING SYSTEMS . 9 The equation s o f motio n ar e nonlinea r an d s o on e typicall y linearize s th e equations abou t a fixed solution . Fo r example , on e solutio n t o th e equation s corresponds t o horizontal flight a t 40,00 0 ft an d 77 4 ft/sec an d th e equation s fo r small latera l perturbation s fro m thi s trajector y ar e (1.4) .9968 .080 2 .0415 ] T^ l / .115 -.031 8 0 r .388 - .465 0 0 \\p .0805 1 0 I \q J V ° J PI r P J_ - .055 8 .598 -3.05 0 + .0073 \ .175 .153 6r, y = [ 0 1 0 0] The 6 r —* r transfe r functio n i s r{s) (1.5) G(s) = .475(8 + .498)( s + .01 2 ± j.488 ) 6r(s) (s + .0073) (s + .563) (s + .03 3 ± j.947) so that th e syste m ha s tw o stabl e rea l pole s an d a pai r o f stable comple x pole s referred t o as the "Dutch roll? Th e stabl e rea l poles are referred t o as the spiral mode (p i = -.0073 ) an d th e roll mod e (s2 = -.563) . Fro m lookin g a t th e natural roots , w e se e tha t th e offendin g mod e tha t need s repai r fo r goo d pilo t handling i s the Dutc h rol l o r th e root s a t s = -.03 3 ±j.95. Th e root s hav e a n acceptable frequenc y bu t thei r dampin g o f ~ .0 3 i s fa r short 3 o f th e desire d Connecting systems . A system with frequency respons e function P i s ofte n associated wit h th e diagra m A common connectio n o f two systems i s and it s transfe r functio n i s QP s o it i s equivalent t o QP 3 This say s tha t G(s) ha s pole s to o clos e t o th e R.H.P . Th e -.007 3 pol e doe s no t matter , because i t ha s n o imaginar y componen t an d therefor e cause s n o oscillation , an d th e pilo t ca n compensate fo r i t easil y himself .
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