⁄
⁄
!g = !s¡pΩ
IR qr!g = MsrL ˆdr
Φ Φrfi rfl
fi fl
0 1 0 1˙` ¡a` ¡pΩ` +aM irfi rfi rfl sr sfi
B˙ C B C` ¡a` +pΩ` +aM irfl rfl rfi sr sflB C B C
B˙ C B C= b(a` +pΩ` )¡ iisfi rfi rfl sfiB C B C
@ A @ A˙ b(a` ¡pΩ` )¡ ii rfl rfi sflsfl
˙ m(` i ¡` i )¡cΩΩ rfi sfl rfl sfi
0 1
0 0 0 0 1B C0 0 0 usfiB C
B C@ A+ m 0 0 u1 sflB C
@ A0 m 0 T1 l
10 0 ¡J
i ;i ;` ;` ;u ;u ;Ω Tsfi sfl rfi rfl sfi sfl l
a b c m
m1 ‡ ·
2 2L R +M Rs rr sra = (R =L ) b = (M = L L ) c = (f =J) = = (1¡(M =L L )) m =r r sr s r v 2 sr s rL Ls r
(pM =JL ) m =(1= L )sr r 1 s
R R L Ls r s r
M psr
J fv
˙X = A (v;X )X +g (v;X ;X )1 1 2 1 1 1 2
y = C X1 1 1
˙X = A X +g (v;X ;X )2 2 2 2 1 2
y = C X2 2 2
v
0 1
0 bp` 0rfl
1@ AA (v;X )= 0 0 ¡ ;1 2 J
0 0 0
0 1
¡ 0 ab
@ AA = 0 ¡a 0 ;2
¡ab 0 ¡a
0 1
¡ i +ab` +m usfl rfi 1 sfi
@ Ag (v;X ;X )= m(` i ¡` i )¡cΩ ;1 1 2 rfi sfl rfl sfi
0
0 1
¡bpΩ` +m urfi 1 sfl
@ Ag (v;X ;X )= ¡pΩ` +aM i ;2 2 1 rfl sr sfi
pΩ` +a(M +b)irfi sr sfl
X = col(x ;x ;x ) x = i x = Ω x = T X = col(x ;x ;x ) x = i1 11 12 13 11 sfi 12 13 l 2 21 22 23 21 sfl¡ ¢
x =` v =x =` C =C = 1 0 022 rfi 23 rfl 1 2
u ` `sfi rfi rfl
ˆ ˆ` `rfi rfl
v
A (v;Z ) Z v1 2 2
g Z v1 2
g Z v Z :2 1 2
¡1 T˙Z = A (v;Z )Z +g (v;Z ;Z )¡S C (y ¡yˆ )1 1 2 1 1 1 2 1 1
T T˙S = ¡ S¡A (v;Z )S¡SA (v;Z )+C C2 1 21
ˆ ˆ ˆkSk Z = col(z ;z ;z ) z = i z = Ω z = T1 11 12 13 11 sfi 12 13 l
¡1 Tˆ ˆ ˆZ =col(z ;z ;z ) z =i z =` v =z =` C =C S C2 21 22 23 21 sfl 22 rfi 23 rfl 1
˙Z = A Z +g (v;Z ;Z )2 2 2 2 2 1