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- Cxa Czu I).l + Cxd Czu Cmq C~ - Cxcr ITIl CmuCI
- Cxq Cl(Czu Cmd Cl + CmurTi\  - Cm i Cza CI)                          (6.23)
Da = -m] Czq CI Cmu - C.u (Cza Cmq CI  - mi Cma - Czq Cmdr C~)
         + Cxa Czu Cmq CI  - Cxtrmi Cmu - Cxdr Cf Cmu Czq
      - CxO(Cz,,Cm ,cl + Cm,mi - Cm"CzaCI)
       .  + Cxq CI(Czu Cm" - Czcr Cmu)                                                      (6.24)
E8 = -Cxa Cmu Czq CI - CxO(Cz"Cm r - Cz"C,"") '               (6.25)
AIRPLANE RESPONSE AND CLOSED-LOOP CONTROL         541
    Steady jy                          
┏━━━━━━━━━━━━━━━━━━┓
┃                      dy Crmvergei  ┃
┣━━━━━━━━━━━━━━━━━━┫
┃t                                   ┃
┗━━━━━━━━━━━━━━━━━━┛
xo
┏━━━━┓
┃XA~     ┃
┃~J ~ ~  ┃
┣━━━━┫
┃        ┃
┗━━━━┛
a) Steady convergence and divergence   b) Undamped (constant amplitude) oscillation
xo
┏━━━━━━━━━━━┓
┃  \ "'7-R -- - -7~ -  ┃
┃~ - - -\z- - -  t     ┃
┣━━━━━━━━━━━┫
┃                      ┃
┗━━━━━━━━━━━┛
c) Damped oscillation
xo
┏━━━━━━━━━━━━━━━━━━┓
┃                           -        ┃
┃                                    ┃
┃          --                        ┃
┃        --                          ┃
┃\--7~ /                             ┃
┣━━━━━━━━━━━━━━━━━━┫
┃/----~j t                 .         ┃
┃                    -               ┃
┃                                .   ┃
┃                                 .  ┃
┗━━━━━━━━━━━━━━━━━━┛
d) Diverging osallation
Fiig.6.1 Typicaldynamicmotions.
  Equation (6.20) is also called the characteristic equation of the longitudinal
motion and gives four values of the root A,. The natu;e of the free response can
be any combination of the typical free responses shown in Fig. 6.1. A steady
convergence corresponds to a real negative root, a steady divergence if the real
root is positive, an oscillatory motion of constant ampli:de if the root is zero, a
　
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