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   CnpAP-(I;i-I;i)Poq+Cnrbi-Iidd)r--0 (7.29)
                                                                                                                                                      .
where
  c          (7.30)
CI = 2Uo
b, = 2~r
Taking Laplace transforms, we get
                            mi Po Aa(s) + (Cyp - mis)Ap(s) - mir (s) = 0
                            (C.zcr - mis) A(x(s) - mi Po Ap(s) + miq(s) = 0
                 Cma Aa(s) + (Cmq Cl - Iyls)q(s) - (Ixl - Izi)Por(s) = 0
                  CnpA,8(s) - (I;I - IAtl)Poq(s) + (Cnrbi - Izis)r (s) = O
(7.31)
(7.32)
(7.33)
(7.34)
(7.35)
INERTIA COUPLING AND SPIN
For a nontrivial solution of these equations, we must have
   miPo   (Cyp-uiis)    O       -mi
.  (Czu -itiis)     -miPo           mi               0
       Cmu           0       (CmqCJ -IyIS)  -(Ixi -Izi)Po
   O     Cnp   -(I;j-I;.i)po (Cnrbi~/;is)
    Expanding the determinant, we get the characteristic equation
                            AiS4 + BiS3 + CIS2 + Dis + Ei - 0
where
Ai = Fyl2tlyll;l                                           .
 Bi  = -m:t(lyiC,,r bi +I;IC,nqCI) - 17ZllyICICzr,r - ITIiCyplyil;l
 Cl  = /Ti:pg-Iy I I;l  + Cyp [lTl I (Iyl Cnr bi  + I;  Cmq Cl) + Iy I Iztl Cztr]
633
-0 (7.36)
(7.37)
(7.38)
(7.39)
             - mi [mi pg-(lri  - lzl)(l;,l -  I;1) - Czu(lyICnrbl + IzlCmqCl)
            - mi Cmqci Cnrbi + mi Cma,l;l] + tTi:lyl Cnp                                       (7,40)
Di  =  _ITI21 pg(lyl Cnr bi + I;I Cmq CI) + Cyp [-Cza(lyi Cnrbi  + Iz I Cmq CI)
               + m{ pg-(lxl  - Izl)(l):l  - I;-I) - ITI ICmqCICnr bi  + mi Cma I/l]
               - mi  [CzaCmq CI C,,rbi  - mi Cma C,,rbi  - (Ix I  - /zl)(/;l  - I;l )Czcr P~]
               - lTZICnp(IT11CmqCI + Czalyl)                                                                             (7.41)
Ei  = mf(lzl - Ixl)(lyl - Ki)P~ - pg [_m21Cmqci Cnrbi + l7~Cnp(lzl - Ixl)
　
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