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- 祠潢 松
- 7 years ago
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Transcription
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14 r xy = = ( x x)( y y) ( x x) ( y y) = = x y x = x = y = y rxy x y = Lxy = x x y y = xy x y ( )( ) = = = = Lxx = x x = x x x ( ) = = = Lyy = y y = y y ( ) = = =
15 r xy Lxy = ( ) L L xx yy 0 Lxy = x y x 0 y = r xy = = = 0 0 Lxx = x x = 0 = = 0 0 Lyy = y y = 0 = = Lxy = = = L L xx yy r rr r r r R = ( 3) Μ Μ Μ r rr
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17 R y d = R - R x y 6 d = r = xy ( 4) ( ) - 3 = 9 - = 4360 d = d = rxy = = 6 34 = 076. ( ) =
18 d = ( R R )
19 r r r r r 3 3 R = r r r3 = r r3 r r r r r
20 r 3 r 3 3 = = r = r r r ( r )( r r ) r r r ( r )( r ) r - r r (- r )( - r ) 3 r 34 r 34 = = r r r ( r )( r ) 43 r r r ( r )( r ) 4 34 ( 5) ( 6) ( 7) ( 8) ( 9) r r r 43 r = = = = r r r ( r )( r ) 3 r r T ( r )( r ) 4 r r T ( r )( r ) 3 r r T ( r )( r ) r r r3 r r r r r R = = r3 r3 r33 r r4 r4 r43 r
21 r 3 = r r3r3 = ( r )( r ) ( 059. ) ( )( 059. ) 3 = 08. r r r r 34 = = = 070. ( r )( r ) ( )( ) r 34 m t = m 5 r 34m
22 t = = R = ( r )( r ) ( 6) y y y R = ( r )( r )( r ) ( 7) y3 y y y3 R = ( r )( r ) [ r ] y k y 8 y yk( k ) R = ( r )( r )( r ) = = ( )( )[ ( ) ] Ry k k F = ( 9) R k yk
23 F = =
24 x y y y y e = y - y y y y y e Q = e = ( y y ) = = = ( y a bx ) m ( 3) = Q = ( y a bx ) = 0 a = Q = y a bx x = ( ) 0 b =
25 ( y a bx ) = 0 = ( y a bx ) x = 0 = a + x b y = = = x a + ( 4) x b xy = = = = x a y = = x x = 4 b xy = = = a = y b x ( 5) Lxy b = = Lx x = = ( x x)( y y) = ( x x) xy x y = = = = x x = 5 6 x y x y = x = xy = y = = a b a b -, ( 6)
26 Lxy b = = L xx 0 = 0 xy x 0 y 0 0 = x 0 = = 0 = x = 0 = ( 40) 0 a = y bx = = y = x 7 y y S = L = ( y y) yy = S = L = yy ( y y) = ( y y ) + ( y y) = Q+ U = = = 9 Q = ( y y ) = N = = 8 ( 9) U = ( y y) = ( a + bx a bx) = b ( x x) = b Lxx = bl = Q F = U / ( 0 ) xy
27 0 S = L = yy y y = ( ) = Q F = U / = = y = b 0 + bx + bx + + b kx k Q = ( y y ) a= a a = [ y ( b + b x + b x + + b x )] a= m a 0 a a k a k Q = y y b ( a ) = 0 a 0 a= Q = ya y x k a a = 0 = ( ) (,,, ) b a=
28 b 0 + xa b xa b x b y ak k a + a + + a = = = a= a= xa b0 + xa b xa xa b xaxa a + a + + a = = = = a= bk xaya a= xa b0 xaxa b ( xa) b xaxak bk = xaya ( 5) a= a= a= a= a= x a b + xax k 0 a + k a= + + b xa xa b b = x y k ak k a k a a= a= a= x x x k x x xk X = x x x 3 3 3k x x x x x xk x x x3 x x x x k T A = X X = x x x x x x x k x x x x x x x k k 3k k k k x a xa xa k a= a= a= xa xa xa xa x x a ak a= a= a= a= N = xa x a xa xa xa x ak a= a= a= A= xak xa xak xax ak x ak a= a= a= y y Y = y a= b 0 b b = b b
29 ya a y = x x x x y x y 3 a a a= T B X Y x x x x y = = 3 3 = xa y a Μ a= x x x x y k k 3k k Μ xak y a L = L = ( x x )( x x ) a a= a= = x a xa xa xa k (, =,,, ) a= L = ( x x )( y y) y a a a= a= a= = xa ya xa ya k ( =,,, ) a= a= a= Lb + L b + L kb k = Ly Lb + Lb + L k bk = Ly ( 5) Lkb + Lk b + L kkb k = Lky b0 = y b x b x b x bk x k
30 x x x x X = x x = Μ Μ Μ Μ Μ Μ x, x , y y Y = y = Μ Μ y b T T b = b X X X Y b = = ( ) y = x x 7
31 U = ( y y) = b L a= = k Q = ( y y ) = L U a= a a yy U / K F = ( 8) Q / ( K ) 4 a= S = L yy = ( y y) =. a U / K F = Q / ( - K -) = U / Q / = / / = y
32 4 = a + b y = x = y x y x 5 S y = y = -x -x x = e a + be y k y = dx x x y = lyx = lxx = lx x k = lxk y = 0 + x + x + + kxk y = yx = lx x = lx x = lx k k y = + x + x + + x 0 k k k k x = xx = x x = x y = y y = + x + x + + x k 0 k k
33 9 y = y x = lx x = lx y = + x + x a= a= 7 a ; ( a ). 3464; a= - 9 x = x =.4980 = a x x 7 7 a 7 = 4.84 y = y = L = x x = 7 a= 7 a a a= L = L = (x - x )(x - x ) = a a= 7 y ( xa x )( ya y ) a= L = (x - x ) = L = = L = (x - x )(y - y ) = y a a= a.3464b b = b b = b0 = b- 4.84b b0 = b= b = y = x x
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35 x x x x Μ Μ m x x, x x x x, x x Μ Μ Μ Μ x x, x x Μ Μ Μ Μ x x, x x m =,,, m x = x / x ( ) =,,, = m x x = ( =,,, ) = x x =,,, m x = s =,,, ( )
36 x m m = m x, S = x x m( ) = = x 0 x m m m x S = = 0, = x x = m( ) = = x =,,, m x = max{ x } =,,, x x m{ x} = max{ x } m{ x } =,,, m =,,, ( 3) 4
37 d = xk x k (, =,,, m) ( 5) k= d = ( xk x k ) (, =,,, m) 6 k= p p d = xk x k (, =,,, m) 7 k= d = max x x (, =,,, m) 8 k k
38 D = ( d ) = ( x k x k) k= r = cos = = m 0 xk k= k= r = k= x k ( x x )( x x ) k k ( x x ) ( x x ) k k= k= k (, =,,, m) x x R = ( r ) =
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44 = a d + a d + d - d 5 d kr p pk q qk pk qk = = 5 D = a D + a D + D D 6 kr p kp p kq kp kq
45 x x xp x x xp X = Μ Μ Μ x x x p x = lx + lx +, + lpx p x = l x + l x +, + lpx p ( ) zm = l mx + l mx +, + l mpx p
46 r r rp r r r p R = 3 Μ Μ Μ rp rp r pp r = k= ( x x )( x x ) k k ( x x ) ( x x ) k k= k= k 4 z r / ( =,,, p) / p k k k= k= k= p z x = e k = p 5 k k k z z zm z z zm Z = 6 Μ Μ Μ z z z m m p k
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51 P P p P P P P = Μ Μ Μ P P P
52 0 P = ( 3) P = = = = [x x x ] x 0 x x = =
53 P = P E E = P E E = 3 5 = P = P E E = P E E = 7 5 = P = P E E = P E E = 7 3 = P = P E E = P E E = 3 = P = P E E = P E E = 4 3 = P = P E E = P E E = 4 = P = P E E = P E E = 5 = P = P E E = P E E = = P = ( 5) N J= k = 6 ( k ) = ( k -)P ( = ) (7) = ( ) = ( 0)P ( ) = ( )P = 0 P ( 8) Μ ( k) = ( k -)P = = ( 0)Pk
54 = lm k = 9 k = [lm k lm k lm k ] k k k = lm k ( 0) k lm k = lm k + = k k lm k + = lm k P k k
55 3 = = [ 3] = [ 3] = = ( 3) 3 =
56 b = a = b m x = b ( =,,, ) = x = a ( =,,, m) = x0 ( =,,, m; =,,, ) z = m = = c x m m = =
57 ax b ( =,,, m) = x 0 ( =,,, ) Z = = c x max ax b ( =,,, m) = x 0 ( =,,, ) Z = x m = ax (, = ) b ( =,,, m) ( ) =
58 x 0 ( =,,, ) ( ) Z = c x m(max) ( 3) = a a a a a a A = Μ Μ Μ a m a m a m ax + a x + + ax = b a x + a x + + a x = b ( 4) a mx + a mx + + a mx = bm N Z = c x ( 6) = ax = b ( =,,, m) ( 4) = N Z = c x m ( 6) =
59 mz = c x = ax = b ( =,,, m) = x 0 ( =,,, ) mz = CX AX = b X 0 a x + a x + + a x b k k k k z = c x = x c + ox + = k =
60 a a am a a a m B = = [ p, p, pm ] ( 8) Μ Μ Μ a a a m m mm
61 CBB A C Z CBB b 0 B A X = B b C BB b CBB A C B b 0 B A ( 6)
62 C B b CBB A C B b B A b b b b b b B A = bm b m bm b 00 b 0 b0 b0 b0 b b b T( B) = b b b b 0 Μ Μ Μ Μ b m0 bm bm b m = m b = b b b s 0 s b 0 r0 rs
63 x + 3x x + x9 x 0 x 0 x + 3x + x 3 = x + x + x 4 = 9 x x x3 x4 0 A = 3 0 p p p = = 3 =,,, 3 0 0, 0 p4 = b C =, 9, = [,,, ] - B = [p p ] B b = b 0 B B B - C B b = 0 C B A - C = -CB A = A B 3 x p = = m{ 3, 9 } = 4 r = ( ) 3 0 p p3 B = p p 4 =
64 b 0 = B 3 = p p =
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66 60x 0x5 00x x 60x x + 500x 4380x5 095x5 0x7 0 50x + 55x 433x5 730x x + x + x 3 65 x x3 650 x4 00 x x x + 3x + 3x3 + x x + 0x3 + 80x x7 + 80x x0 ( =,,, 8)
67 max Z = c x ( ) = ax b ( =,,, m) ( ) = x 0 ( =,,, ) ( 3) m ayc ( =,, ) = W = m = b y m m W = by ( 4) = m ayc ( =,,, ) ( 5) = y0 ( =,,, m) ( 6) maxz = CX ( ) AXb X0
68 mw = Yb ( ) YAC Y0 x y x x x mw y y Μ y m a a a a a a Μ Μ Μ a a a m m m Μ maxz C C C maxz=mw b b Μ b m max Z = c x = ax = b ( =,,, m) = x 0 ( =,,, )
69 max Z = c x ( 7) = ax b ( 8) = ( a ) x b ( 9) = x 0 ( =,, ) ( 0) y y = m 8 m m m W = by + ( by ) = = m m ay + ( a y ) c ( =,,, m) = = y 0, y 0 ( =,, m) m m W = b( y y ) = m a( y y ) c ( =,,, ) = y 0, y 0 ( =,,, m) y = y y y 0 y 0 y y m mw = b y = m ay c ( =,,, ) = y ( =,,, m)
70 mz = x + 3x 5x 3 + x4 x + x 3x 3 + x45 x + x3 x44 x + x3 + x4 = 6 x0 ; x, x3 0 ; x4 max Z= 5y + 4y + 6y3 y + y y + y 33 3y + y + y3 5 y y + y3 = y0, y 0, y 3 X Y cxyb
71 maxz = cx AX + Xs = b X 0 Xs 0 mw = Yb YA - Ys = c Y 0 Ys 0 7 X Y Y Xs = 0YsX = 0 X Y max Z = OX AX = b X 0
72 - - m B b B b 0 = B b - C Z = = Ck Zk m a l 0 al a lk mw = x + 3x + 4x3 x + x + x33 x - x + 3x4 x x x3 0 maxz = -x - 3x - 4x3 - x - x - x 3 + x 4 = -3 - x + x - 3x + x = x 0 = 5 l
73 - - m B b B b 0 C Z = = 4 m al 0 m, a l 3 = =
74 Μ m a a Μ a m b b b Μ m C C C C C C Μ Μ C C C Μ m C C C C C C Μ Μ C C C a a Μ a m b b b
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80 A A A B B B B A A A B B B B u 4 v
81 B B B B A A A A A A B B B B 0 9 m a = b ( 6) = =
82 m a b = = m Z = c x ( 8) m = = xa ( =,,, m) ( 9) = m x = b ( =,,, ) ( 0) = x0 ( =,,, m, =,,, ) ( ) m + (7) x + x, + = x = a( =,,, m) ( ) = = x = b ( =,,, ) ( 3) = m m x + = a b = b+ = = =, ( 4) mz = cx = c x = m = = + m = = c x m, +, + = + x = a( =,,, m) ( 9) = m x = b ( =,,,, + ) ( 0) = x0 ( =,,, m; =,,,, + ) ( ) ( 8)
83 m + a = b + b + = b = = = ( ) m a b = = = m + b a = m =
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85 k = max ψ = λ ψ ( 9) k λ = = ( ) * * f f f k = * m Z = a ( f f ) 4 f * I
86 k + mz = ( f + f ) ( 8) = f + f f + = f * ( =,,, m ) ( 0 ) f + * f f f. T + - mz = v F + F X G - + * F + F - F = F 3 ϕ ( x, x,, x ) g ( =,,, m) ( 5) m max f f f = 3 K ( 6) m F F F ( ) max 9
87 x + x x + x0 3 x x 0 4 * * x = 4 x = 3 Z* = 6
88 mz = Pd + P (d + d ) + P3d x - x + d - d = x + x + d - d = x +0x + d - d = x x d d 0 = 3 4 3
89 + k L + + m Z = Pk( kld l + kld l ( 5) k= l= ( l) c x + d l d + l = g l( l =,,, L) ( 6) = ax ( =, ) bl ( =,, m ) ( 7) = + d, d 0 ( l =,,, L) ( 9) l l + kl kl kl kl P l + - g x d d k c (l) c - Z 0 k C - Z = a P ( = P >> P >> P k k k k= l l a
90 mz = Pd + P (d + d ) + P3d x - x + d - d = x + x + d - d = x +0x + d - d = x d d = x 3 3 d d d 3 = m, 0, = 0 - d 4 * * x = x = d d d 3 * * x = 0 / 3x = 0/ 3
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93 SO Cl NO NO Cu Pb pv 4 3
94 SO Cl NO NO Cu Pb 4 3
95 PI w c = ( 6) S = c( r,, z) PIW = PI W( r,, z) = 3 ( 7 ) s =
96 8 8 3 =.8
97 3 = + a x + d d = b a = =,,, 3 3 J= + a x + d = d = b 993
98 a =
99 = a 3 + a x + d d = b =,,, 3 3 = a 4 = + a x + d d = b =,,, 3 3 = a 5 = + a x + d d = b =,,, 3 3 = a 6 = + a x + d d = b =,,, 3 3 = a 7 = + a x + d d = b =,,, 3 3 = a 8 = + a x + d d = b =,,, 3 3 =
100 = a 3 9 a + a x + d d = b = =,,, 3 3 = 0 + a x + d d = b = =,,, 3 = a 3 + a x + d d = b = =,,, 3 3 cx = B =,,, 3 = 0 c = - d = =
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111 E( A ) = a P ( =,,, m) ( ) = A E( A) P A E A ( P A = E A = ), ( ), P =, Μ Μ Μ A m E( A m) P a a a a a a B = Λ Λ Λ Λ Λ Λ Λ Λ Λ a a a m m m 0. A A 0. A = P B A = = A E( A) E( A ) E( A) = BP E( A ) = 3 E( A ) = = EA = max E A = 83 / 3
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116 () max V(A () max max V A VA max maxv ( A ) * * max{v( A )} = max{ } 0 / = V A 5 max V A = max = 50 / = V A
117 max V A = max = 30 / = V( A3 3) max V A = max = 9 / = V A4 5 max max = max = 50 / = V A max max V A = V A m V max m V A VA = maxm{v A } * * m{va } = m{ } = 00 ( / ) = W(A, ) m V A = m = 80 / = V A 5 m V A = m = 0 / = V A 3 5 m V A = m = 8 / = V A 4 max m V A = max = 8 / = V A 4
118 max m V A = V A 4 max V m{v A V = max{v A + - m V A 4 max{v } V = max V * max V A = max = 0 / = V A 5 max V A = max = 50 / = V A max V A = max = 30 / = V A3 3 max{va } = max = 0 / = V A 4 5 m V A = m = 00 / = V A m{va } = m = 80 / = V A 5
119 m V A = m = 0 / = V A 3 5 m V A = m = 8 / = V A 4 max V = max = 70 / = V3 max{ V } V = 3 P = P = = P = P = P = P = P = P = E( A) = = 65. ( / ) E( A) = = 66( / ) E( A3) = = 60( / )
120 E( A4) = = 636. ( / ) max E A = 66 / = E A max{v A } = VA * V = VA - V A * 3 max V } 4 m max{v } m maxv } = V ** max{v A } = max{005008} max V A = max max V A = max max{va } = max{ max{v A } = max{ } 5 = 0 / = V A 5
121 max V = max = 50 / = V max V = max = 40 / = V5 max V = max = 30 / = V3 max V = max = 3 / = V4 m max{v } = m } = 30 / = V m max V = V 3 3
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123 W / W W / W Μ W / W W / W W / W Μ W / W A = Μ W/ W W / W Μ W / W
124 b = 3 b = (, =,,, ) b bk b = (,, k =,, 3,, ) 4 b k λ CI = max 6
125 CR = CI RI T b b b B A, b = 0), m a b = = = 8 CI = RI = m = m = a CI 9 a RI 0 CR = CI RI
126 M b ( =,,, ) ( ) = W = M ( =,,, ) (3) 7 3 W = [ W, W,, W ] W = W / W ( =,,, ) (4) = ( ) λ max = AW 5 = W b = b / b (, =,,, ) k k= 6 W = b ( =,,, ) = 7 T 3 W[ W, W,, W ] W = = W ( =,,, ) ( 8) W =
127 (AW) λ max = (9) = W
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140 V V E E e E V, g g gm g g gm L( G) = ( ) g g g L( G) =
141 a a a a a a A( G) = ( 3) a a a A( G) = = m ( 4) = P ( 5) -
142 m + P = ( 7) 5P m + P = 00% (8) 5P m = 9 3( P) m = 00% ( 0) 3( P)
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146 d d d3 d4 d5 d d d d 3 d 4 d 5 d d d d d d d D = = d 4 d4 d43 d 44 d45 d d d d d d d d 6 d6 d63 d 64 d65 d S( v0) = m S( v ) = m a( v ) d ( ) = d d d d d d d d d d d d d d d d d d d d d D = d d d d d d d d d d d d d d d d d d d d d d d d d d d d
147 = S( v ) = a( v ) d =. 3 = 7 S( v ) = a( v ) d = 73. = 7 S( v ) = a( v ) d = J= 7 S( v ) = a( v ) d = = 7 S( v ) = a( v ) d = = 7 S( v ) = a( v ) d = = 7 S( v ) = S( v ) = m{ S( v )} 3 4 S( v ) = a( v ) d = = 7 = m a( v ) d = =
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149 m u v s t ( u, v) P p m r u v 7-9 ( u, v) P
150 c s c I s a a b I b a R d d a a
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152 f s a = = m s a s a I s a R r c - f a c = 4-0 = 4 a c R c t - f c t = - 0 = c t R f s a = = m s a s a I s a R r f b t = = m b t b t I b t R f c t = = m c t c t I c t R
153 m c u v f u v 5 ( u, v) fs v - f u s = Q 6 v v v f u v - f v u = 0 u s u t 7 ft u - f v t = -Q 8 0f u v m u v u v E 9 maxpq - u v f u v 0 (u,v)
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162 W( s ) = Y(s) X(s)
163 d Y d Y a a dy a 0Y dt dt dt b X b dx m d X b b d m = X 0 m m + m m ( ) dt dt dt m m Y( s) b0 + bs + + b m s + bms W( s) = = ( 3) X( s) s + a s + + a s+ a 0 W3 ( s) X 3 ( s) X ( s) W( S) = = = W ( s) W ( s) ( 4) X ( s) X ( s) X ( s) Ws = W (s) W (s) W (s) = W (s) (5) =
164 W s = X 4 ( s ) = W ( s) + W ( s) ( 6) X ( s) W(s) = W (s) + W ( s) W ( s) W ( s) ( ) + + = 7 = C( s) = R( s ) + X( s) X( s ) = C( s) W( s) C( s) = e( s) W( s) R(s) = e(s) - X(s) = e(s) - C(s) W (s) = e(s) - e(s) W(s) W(s) = [- W (s)w (s)]e(s)
165 C( s) e( s) W ( s) W( s) = = R( s) [ W ( s) W ( s)] e ( s) W ( s) = W ( s) W ( s) e( s) = R( s) - X( s) X( s) = C( s)w ( s) C(s) = e(s)w (s) R(s) = e(s) + X(s) = e(s) + C(s)W (s) = e(s) + e(s)w (s)w (s) = [+ W (s)w (s)]e(s) C( s) W ( s) e( s) W( s) = = R( s) [ + W ( s) W ( s) e( s)] W ( s) = + W ( s) W ( s) 8 9 [ W ( s) W5 ( s) + W ( s) W6 ( s) + W3 ( s) W7 ( s) + W4 ( s) W8 ( s)] W( s) = E( s)[ W ( s) W ( s) + W ( s) W ( s) + W ( s) W ( s) + W ( s) W ( s)]
166 dx = F ( x, u) dt ( 0) Y( t) = G( x, u) x = A( t) x + B( t) u ( ) Y = C( t) x + D( t) u x y ( ) x y X = = Μ Μ ( ) x y x& = y& = x x = y& = x4 x& 3 = y& = x3 Μ ( ) x & = y = x ( ) ( ) ( ) x& y u a y a y a y& = = a y = u ax a x a x a x A = Μ Μ Μ Μ B = Μ a a a a
167 &X = Ax + Bu 3 x& = Ax + Bu ( 5) y = Cx X(t +) = (t +t)x(t) + F(t)U(t) ( 6) Y(t)= H(t)X(t) + G(t)U(t) X(t +) = (t +t)x(t) + F(t)U(t +) ( 7) Y(t)= H(t)X(t) + G(t)U(t)Y(t) = H(t)X(t)+ G(t)U(t) x( t) x ( t) X () = ( 8) Μ x ( t) u u(t) (t) u(t) = u (t)
168 ), e, e = e. = e x (t +) = (+ r )x (t) + = + x (t)- x (t) ( = ) (9) 0 0 x ( t) x ( t) = e x0( t) = ( 0) e x 0( t) = = e = e u( t) ( ) x t k e ( ) = x ( t) ( ) r x (t) = k e r x t r k e ( + ) = ( + ) x ( t) = r (t) (3) k e x t r ee u t e + ( ) + ( ) u( t) = e = ( =,,, ) ( 4) =
169 = = = = ( ) ( ) ( ) r k e r k e r k e e k e r r k e r k e r k e r k e r r k e r F e e e e e e e e e e e e = = = = = = = Μ Μ
170 dx = f (x x x u u u m) dt = t 0 tt () dx = F(XU) t 0 tt () dt f ( x, xx ; u, u, um ) ( = ) x u x ϕ (x u) 0 = l(l m) (3)
171 (0) X(t ) = X () X ( 0) 0 X (0) max(m)j[u(t)]= max(m){g[x(t) T] T t 0 0 * + f [X(t) U(t)]dt} = J[U (t)] (8) o x (T) = xt = k (0 k ) (6 ) H[X(tU(t (t ] = f [X(t U(t)] λ (t)f [X(t) U(t)] (9) = dλ f dt = H λ x = - x (0) ( =,,, ) = ( ) [ ( t)] 0( ) 0 = λ
172 dx = H = f (X(t) U(t)) ( = ) () dt λ H[X(t) U(t) (t)] = max H[X(t) U(t) (t)] (3) U U t dx = F(x) - u(t) dt ( 6) x(0) = x 0 J = [P - C(x)]u(t)dt (9)
173 + -bt J(u) = E [ P C( x) u( t) dt] (0) 0 dρ( x) = [ ρ C( x)] ( ) dx * u max x x * * * u ( t) = F( x ) x = x * u m x x F(x) = rx(- x K ) () C(x) = C (3) x * K C C C δ δ 8δ x = ( 4) 4 PK r PK r δ u m x x * * * x * u ( t) = rx x = x * K u max x x*
174
175 x(k +) = A + B x(k) u(k) ( ) y(k) = Cx(k)
176 k J y k r T = [ ( ) Qy( k) + u( k) Ru( k)] ( ) k= 0 B 0 C 0 B C B = C = Ο Ο 0 B 0 C Q Q = O Q N 0 R 0 R R = Ο Ο Q O R N A A AN A A AN A = Μ Μ Ο Μ A N AN ANN N J = J ( 3) = k T T T J = [ x ( k) C Q C x ( k) + u ( k) R u ( k)] k= 0 N x (k +) = Ax (k) + Bu (k) + Ax (k) = ( 5) y (k) = Cx (k) = N A x ( k ) N N = N N
177 m = N = A x x (k + ) = A x (k) + B u (k) + m (k) ( 6) y (k) = Cx (k) N m (k) = Ax ( k ) = N (7) = J = N J = N k T T T J*= x ( k) C QCx( k) + u ( k) Ru( k)] = k= 0 N N T * + (k) A x( k) m ( k) = J (8) = = * J k J = * T T T T [ x ( k) C ( K) C QCx ( k) + u ( k) Ru( k)] k= 0 k N T T + λ ( k) A x ( k) λ ( k) m( k) = N (9) k=0 = Ax (k) = m (k) = N N = N (0) ( k) = m ( k) =,,, N ( ) = x (k +) = Ax (k) + Bx (k) + (k) ( ) y (k) = Cx (k) =,,, N
178 N * J* = J (3) = * (3) J k * T T T J = [ x ( k) C QCx ( k) + u ( k) R u ( k)]] k= 0 k N T T + [ λ ( k) A x ( k) λ ( k) m ( k)] k= 0 = =,,, N ( 4) 5 mf = Cx = 5 w x = (5) = 0 x b ( = 3 4)
179 4 mz = Cx =0 4 w x = 50.5 ( 6) = 0 x b ( = 3 4) L(x, ) = C x + λ wx 505 = L 7). ( = = = (7) L = C x + w x -.65 ( = 3 4) ml = cx w x ( 8) 0 x b ( = 3 4) L λ L k+ k = + a k (9)
180 4 w x = ( 0) = k x ( = 3 4 k = 0 ) 4 () w x, = L k+ k = + k ()
181
182 x A x A C ( A x ) = x A 0 x A ( ) () U A U = x x x A
183 A = = x x x ( 4) = x A = A ( x) / x ( 5) x U () A = B A ( x) = B ( x) x U () A = A ( x) = 0 x U ( 3) A B A ( x) B( x) x U ( 4) A A ( x) = A ( x) x U ( 5) A Υ B A ΥB ( x) = max{ A ( x), B ( x)} = ( x) ( x) U A B B (6) A Ι B A Ι B( x) = m{ A ( x), B ( x)} = ( x) ( x) x U A B (3) ( A Υ B ) Υ C = A Υ( B Υ C) ( A Υ B ) Ι C = A Ι ( B Ι C )
184 (4) A Υ( A Ι B ) = A A Ι ( A Υ B ) = A ( 5) : A Υ( B Ι C ) = ( A Υ B)( A Υ C) A Ι ( B Υ C ) = ( A Ι B) Υ( A Ι C) (6) A = A (7) De Morga A Υ B = A Ι B A Ι B = A Υ B ( 8) : A ΥU = U A Ι U = A A a = x A (x) x U (7) () A A A a Aa A a ( A Ι B ) a = Aa Ι Ba, ( A Υ B) a = A ΥB a a ( A Ι B ) a = Aa Ι Ba, ( A Ι B) = A Ι B a a a (5) Υ A = A, Ι A = A (6) Ι A = A, Ι A = A (7) A = Υ A (8) [0,]
185 (8) A a x A ( x) = A 0 x A R U V (x y) U V R(x y) U = V R U U V R r r r r r r R = ( r ) = m r r r m m m I (x y) = x = y I x, y U 0 x y O (xy) = 0 x y U o (3) E E E (xy) = x y U (4) R T T R T R (xy) = R (yx) x y U
186 U V W R U V R V W RοR R R U R οr (xz) = V[ (x y) (y z)] R R ( RοR) οr3 = Rο( R οr3 ) I ο R = R οi = R O ο R = R οo = 0 R R RοR RοR, Rο R T T T ( RοR) = R οr R ο( R Υ R ) = ( R οr) Υ( R οr ), ( R Υ R ) ο R = ( Rο R ) Υ( R ο R ) R ο( R Ι R ) = ( R οr) Ι ( R οr ), ( R Ι R ) ο R = ( Rο R ) Ι ( R ο R ) T T T ( R Υ R ) = R Υ R T T T ( R Ι R ) = R Ι R T T ( R ) = R R U x U R(x x) = x y U R(x y) = R(y x) R U R U x y z R
187 r r r r r r R = (r ) = m r r r m m m ( 0) B = [ b, b, b ] = A ο R m M m = V ( a k r k V a kr k V a kr ), ( ),, ( k ) () k= k= k=
188 R U U U R - R U U R U U R U R* R = r = (, =,,, m) ( ) xkx k / M k= Mmax x k x k k= = r = (, =,,, m) () - c xk x k k=
189 r m( x k, x k) k= = (, =,,, m) (3) max( x, x ) k= r k k m( xk, x k) k= = (, =,,, m) (4) ( xk + x k ) k= - xk -x k k= r = e (, =,,, m) (5) 3 ( x x k k) 4 r e m 6 (, =,,, ) ( ) s k= k s m = x x m( ) k k k =. R R R R R * R R = R R ο 4 R = R οr R k = R k οr k = R k R = R k
190 R = R* = R0 R = R R R * R = * R G G G 3 G 4G 5 Gl G7G 8, G9
191 R R G 5, R = R , R = R
192 R = R , R 0. 8 = R , G, G, R = R 0 87 G G G3 G4G5G6G 7G 8
193 U R = (r ) mm () R m G = (V E) G R =
194 R r r r R R = r r r = (3) Μ Μ Μ Μ R r r r m m m m A = [a a a m ]( A m U 0 a a = ), = B = A ο R = [ b, b,, b ] ( 4) m U = U = ( 5) U Ι U = ( )
195 U A R B = A οb = [bb b (7) B b b b B b b b R = = Μ Μ Μ Μ B b b b m m m m U / c A B = A ο B ( 9) (9) B U / c U (8)
196 A = [a lla a 3a 4 a 5 ] A = [aa a 3a 4a 5] A 3 = [a 3a 3 a 33a 34 a 35]
197 r r r r r r r r r r R = r r r r r r r r r r r r r r r = ( r ) r r r r r r r r r r R = r r r r r r r r r r r r r r r = ( r ) r r r r r r r r r r R = r r r r r r r r r r r r r r r = ( r 3 ) A R B = A οr = [b b b3 b4 b 5] ( = 3) B b b b b b R B b b b b b = B = b b b b b U A R B B = Aο R = [a a a 3] B B3 = [b b b b b ] 3 4 5
198 R = R = R 3 = A = [ ] A = [ ] A = [ ] A 3 = [ B = AR = [ ] B = AR = [ ] B 3 = A3R3 = [ ] R R = R = R3
199 B = Aο R = [ ] B = [ ]
200 S [ T, T ] ( ) S T T 0 ( T) [ 0, ] ( ) S T ST ST T ST S T (t) S R (t) S I (t) T S ( t ) T Sc (t) = SR( t) (3) SI ( t) S C (t)[s T (t) + S R (t) + S I (t)] (4) 3 Sc(t) = [ ST ( t) + SR( t) + S ( t)] / t t [0,t 0 ] 3 (5)
201 SC( t) = [ ST ( t ) + S( t ( 6) = 3 S C (t) S T (t) Ι S R (t) Ι S (t) (7) SC (t) = [S T (t) S R ( t) S (t)] / t (8) t [0,t 0 ] SC (t) = [S T(t ) S R ( t ) S I( t )]/ t (9) = SC3 ( t) ST ( t) + a SR ( t) + a3si ( t) ( 0) S C3 (t) [as T (t) + a S R (t) + S (t)]/ t () t [0,t 0 ] s T R 3 I = Sc ( t) = [ a S ( t ) + a S ( t ) + a S ( t )] / t ( ) t 0 t 9 CT = Sc ( t) dt = [ ST ( t) + SR ( t) + SI( t)] dt ( 3) C T = 3 = [S (t ) + S (t ) +S (t )] (4) T R I t0 t 0 Ce = Sc( t) dt = [ ST( t) S R ( t) S I ( t)] dt ( 5) 0 0 C = [S (t ) S ( t ) S (t )] (6) e T R I =
202
203
204
205
206 m + kmax ( t) = t =,, 3,, M ( ) ( t) + kmax x ( t), = max max ( t), = m m ( t); k [ 0, ] max m (t) max ( t) = ; ( t) max (t) m ( t) = + k k m +, t k ( )., max + m ( ) ( t ) max
207 γ = S S (4) M γ ( t) (6) M = x (t) = x (t) / x () = N t = M (7) t x (t) = x (t) / x = N t = M (8) M (8) x = M x t ( ) =
208 R = = () = = max 4 = 5 3
209 M {x (t)}., (0 ) t= (0) M {x (t)} t= Μ ( ) ( 0) x ( k) = x ( t) Μ t= M ( ) ( 0) x ( M) = x ( t) k t= () M {x (t)} t = { ( 0 ) M x ( t)} = ( ) dx ( ) + ax = u ( ) dt a T T B B B YM u = ( ) ( )
210 - () () [x () + x ()] - () () [x () + x (3)] Μ Μ ( ) ( ) [ x ( M ) + x ( M)] x (t + ) = x e + u () u (0) -at ( ) (3) a a x () (t) (0) () () x (t) = x (t) - x (t -) (4) () (4) t = M x (0) = 0 ( 0) ( 0) ( 0) ( t) = x ( t) x ( t) ( 0) ( t) ( 5) q( t) = ( 0) 00% x ( t) M ( 0) x M x ( 0) = ( t ) s t= M ( ) = ( x ( t) x ) M 0 0 t= M ( ) ( ) ( ) = ( ( t) ) M t= p{ (0) (t) - (0) s } (0) M { (t)} = t
211 0 {x ( )} = {x (0) (q) x (0) (q) } (8)
212 (0) 0 (0) (0) (0) (0) x ( ) = {x ( ) x ( ) x (3 ) x (4 ) x (5 )} = { } (0) (0) (0) (0) (0) = {x (3) x (8) x (0) x (4) x (7)} ( ) dp ( ) + ap = u ( ) dt a T T B B B YM u = ( ) ( )
213 ( ) ( ) [ p ( + p ( ))] 7 ( ) ( ) [ p ( 3) + p ( )] B = = 65. p + p 8 ( ) ( ) [ ( 4) ( 3)] 435. ( ) ( ) [ p ( 5) + p ( 4)] T Y = [ p( ), p( 3), p( 4), p( 5)] M T = [ 8, 0, 4, 7] a. T T : ( B B) B YM u = = ( ) DP () p = (3) DT
214 max(m)z = CX = c () = x ( A) X( =, b ) ( ) X0 ( 3) c ( = ) ; (A) A (A) ( A) = Μ Μ Μ m m m a a a a a a A = Μ Μ Μ a a a m m m [a a ] a a b = [b ( 5) (A) a a [a a ] (0) (0) (0) (0) b = {b () b () b (N)} (6) (0) () () b AGO( ) b b GM( ), (4)
215 (0) b (k)(k N) ( 0) b ( k ) ( 0) b ( k ) ( A) X ( 7) Μ ( 0) b ( k ) m
216 x x 8 x + x 757 x = 500 = = 3 = 4 x x x + + x + x x = = x x
217 8 = 3 x 4 + x x 530 = x + 0.6x x ++ x 8 + x + 0.4x = = = 3 8 x + x 6565, x550, = 8 4 = x + 0.6x x + + x + x + 0.4x , 4 3 = = =
218
219 r s r = ( a, b ) r rm δ = r,,, () s s s m
220 r s r = s Μ r s () r r r m s s sm r r r m M = s s s (3) m Μ Μ Μ r r rm s s s m m + Kmax r (t) = (4) ( t) + Kmax u r = ( 5) u max r = u u m r = m{u u }, 0 (7) max{u, u } 0 (6)
221 u0 r = (8) u0+ u u0 u lm ( ) t = (9) t u a a r = (0) a ( p) r (p) r s ( p) ( p) ( = ) M ( P) (p) ( p) ( p) r r r m s s sm ( p) ( p) ( p) r r r m = s s s m Μ Μ Μ ( p) ( p) ( p) r r r m s s s m () ( p r ) ( ) = a T () l p= p a = a = = a = l () ( ) r = l l p= (p) r ( )
222 ( ) ( ) ( ) r r r m s s sm ( ) ( ) ( ) r r rm ( ) M = s s s (3) m Μ Μ Μ ( ) ( ) ( ) r r rm s s sm ( ) M ( ) ( ) ( ) ( ) ( ) r = maxγ = max{ γ, γ,, γ } ( ) r * s * m 4 ( ) * s b a * * ( ) M ( ) ( ) ( ) ( ) = maxr = max{r, r,, r } (5) r * s ( ) ( ) r * ( ) * s a b * *
223 ( /km ) (%) () () 0-7 u = 390 u = 549 () () () () () u = 776u = 7790u = 499u = 303u = 88u 3 3 () 33 () 3 () () 3 ( ) 3 () ( ) ( ) ( ) 3 33 u = 09 u = 0.37 u = 0.33u 3 = 460, = 05., () () u = 0.3u = 0.9u = 0.45u = 0.33u = 0. 35, u =
224 M ( ) r s r = s r s r s r s r s r s r s r s ( ) ( ) ( ) 3 3 ( ) ( ) ( ) 3 3 ( ) ( ) ( ) s s s = s s s s3 s3 s 33 ( ) ( ) ( ) r r r s s s 3 s s s3 ( ) ( ) ( ) r r r M = = s s s 3 s s s 3 ( ) ( ) ( ) r3 r3 r s s s s3 s3 s ( ) r ( = 3) r s r ( ) M = s r s r s r s r s r s r s r s ( ) ( ) ( ) 3 3 ( ) ( ) ( ) 3 3 ( ) ( ) ( ) s s s = s s s s3 s3 s33
225 X U = W () X U = W (3) + WZ + WZ = W X U - W X = U- ZX (4) WZ W = + W
226 W X = U - G X = U (6) * - _ G G Q * - - Q = G* - G (7) - G* X = U + QX (8) - - G X = U G X = U QX * G* X = u + QX QX G X= u *
227 z z z z z z Z = Μ Μ Μ z z z - - J = G - G = m(s) () u *
228 ( x ) ( )( ) 0 ( 0 x ( )( ) ( 0 x 3 ( )( ) ( 0 x 4 ( )( ) ( 0 x 5 ( )( ) (0) (0). {x ()} {x ()} GM( ), ( 0) ( 0) ( 0) x ( ) + x ( ), x ( ) 4 = = = 3 3 ( 0) ( 0) ( 0) x ( ) + x ( ), x 4 ( ) = = = 304, 9 X(, 4) = = ( 0) ( 0) x ( ) + x ( ) 495., 78 ( 0), x ( ) = = = 74, ( 0) ( 0) ( 0) x ( ) + x ( ), x 4 ( ) = = = (0) (0) (0) (0) T Y = [x () x (3) x (4) x (5)] = [ ] 5 4 a T X X Y b = = [ (, 4)] (, 4) ( ) dx ( ) ( ) x = x4 ( 3) dt () () slaplace x x 4 (0). {x ()} { ( 0 x ) ( )} 3 s
229 a b = ( ) dx3 ( ) ( ) x3 = x5 ( 4) dt (0) (0) (0) 3. {x ()} {x ()} {x ( )} 0 ( 0) ( 0) ( 0) ( 0) x ( ) x ( ), x ( ), x ( ) + 3 = = = = ( 0) ( 0) ( 0) ( 0) x ( ) + x ( ), x ( ), x 3 ( ) X(, 3) = = = = = ( 0) ( 0) ( 0) ( 0) x ( ) + x ( ), x ( ), x 3 ( ) = = = = ( 0) ( 0) ( 0) ( 0) x ( ) + x ( ), x ( ), x 3 ( ) = = = = = (0) (0) (0) Y = [x () x (3) x (4) x (5)] = [ ] 5 (0) T T a T T b = [ X(, 3) X (, 3)] X (, 3) Y 5 = b ( ) dx ( ) ( ) ( ) x = x x3 ( 5) dt 3
230 () 0-6 x 3 ( ) x ( s) 9. 7( s) ( s) = ( ) = 3 u ( s) 05. s s + ( ) s s + ( )s = 0 (7) 3 3 ( ) ( ) ( ) s, = 074. ( ) ( ) ( ) (- 9.7 ), = 0 = = , a = ( ) = = 34 a 3 3 ( ) X 9. 7( s) ( ) = ( 8) U 074. s + ( ) s ( 6)
231 ( ) dx () ( ) + (-9.7 3)x dt () (0) = (9) ( ) ( 0) ( ) ( 0) x ( t) = ( x ( ) cu c u t cu c u e ( ) ( 0) = = ( 0)
232
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235 A + B A B A B A B B
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257 q + q + + q + y = q q + q + + q + y = q Μ Μ Μ Μ Μ q + q + + q + y = q q + q + + q = L 0 0 o Μ q q q q q q Μ Μ Μ q q q m y y Μ y q q Μ q q q q l L
258 = q + y = q ( =,,, ) () = q 0 = L ( ) a = q (, =,,, ) (3) q q0 a 0 = ( =,,, ) ( 4) q = a q + y = q ( =,,, ) ( 5) = a q 0 = L a a a A = a a a a a a a a a a a a ( I A) = a a a ( 6)
259 x + x + + x + y = x x + x + x + y = x Μ Μ Μ Μ Μ x + x + + x + y = x x + y = x ( =,,, ) ( 0) = x a = (, =,,, ) ( ) x a x y x + = ( =,,, ) () =
260 a a a a a a A = a a a x + x + + x + V + m = x x + x + + x + V + m = x Μ Μ Μ Μ Μ Μ x + x + + x + V + m = x x + V + m = x ( =,,, ) ( 5) = a x N x + = ( =,,, ) (6) = a = (6) a 0 0 = a C = 0 0 = Μ Μ Μ 0 0 a =
261
262
263 Μ x x x x x x Μ Μ Μ x x x y y Μ y Μ m u u u u u u Μ Μ Μ u u u m w w Μ w x + y = x ( =,,, ) ( ) = a x y x + = ( =,,, ) () = u + w = u ( =,,, m) ( 3) = d = u =,,, m x =,,, (4)
264 dx + w = u ( =,,, m) ( 5) = m x + u + v + m = x ( =,,, ) ( 6) = = m ax + d x + v + m = x ( =,,, ) ( 7) = = d d d d d d D = Μ Μ Μ d d d m m m m d 0 0 = m D = 0 d 0 = m 0 0 d = (C + D)X + V + M = X (0)
265 x pq p q y pq p q q p, q = m+ y p y po p y po = m+ q= y pq y qp q y pq = m p= y pq q q q v m x q m m p =,,, m pq po p x + y = x ( 3) =,,, q= = m q =,,, m pq q q q x + v + m = x ( 4) =,,, p= = pq a q pq x p q m pq, =,,, a = q ( 5) x, =,,,
266 m p =,,, m pq q po p a x + y = x =,,, m p= = q= = pq q q q a x + v + m = x q q =,,, m =,,, (7) m (6) A pq X q + Y PO = X p ( p =,,, m ) (8) q= q q q q q B X + V + M = X (q = m) (9) pq pq pq a a a pq pq pq a a a pq A = Μ Μ Μ pq pq pq a a a ( p, q =,,, m) m pq a 0 0 p= = m pq 0 a q 0 B = p= = Μ Μ Μ m pq 0 0 a p= = m A A A m A A A A = Μ Μ Μ m m mm A A A B 0 0 B 0 B 0 = Μ Μ Μ 0 0 B m
267 X X X =, Μ m X V V V =, Μ m V 0 Y 0 Y Y = Μ m0 Y M M M = Μ m M BX + V + M = X () q =,,, m x oq q qo oq = ax + y ( ) =,,, x po x = oq = m q= = m x p= pq x pq p =,,, m =,,, q =,, m =,,, ( 3) ( 4) oq qo () x q x q q a q, y oq q q m m p= q= pq oq oo x = xpo = x = x ( =,,, ) ( 5) m m p= q= x oo
268 po oq x x pq pq x = oo Q ( p, q =,,, m; =,,, ) ( 6) x pq (6) Q pq p q pq pq Q = ( c + k ) d δ ( 7) pq (7) d p q p q 0 c k pq x x pq po oq p oq x x x x pq p q = oo Q = oo ( c + k ) d x x pq p q = b ( c + k ) ( 8) po oq oq oo (8) x x, x x pq δ pq po x pq pq pq b = oo d δ ( 9) x m m pq pq = [ x x ] p= q= m m pq pq p p q = [ x b ( c ( c + k )] ( =,,, ) ( 30) p= q= p p c k (30) m pq pq q q pq p = x b c k b c [ ( + )]( ) = 0 q= ( 3) m pq pq p q pq q = x b c + k b = [ ( )]( ) 0 k p= p m m c q (p = m) k (q = m)
269 Μ Μ Μ k Μ m x x x x x x x x x x x x Μ Μ Μ Μ x x x x c c c c c c c c Μ Μ Μ Μ c c c c k k k k Μ Μ Μ Μ c c c c m m m m y y y y Μ Μ x x x x Μ Μ
270 () () A a = x x - 5 d = c x ( = m = k d d d d d d D = d d d m m m max Z = (x -a x ) (4) = = max Z = x (5) = max Z = y (6) = max Z = p y (7) =
271 ( I A) X = Y DXB ( 8) X0, Y0
272 Μ Μ m m x x x E E E m y x x x E E E y m Μ Μ Μ Μ Μ Μ Μ x x x E E E P P P P P P Μ Μ Μ P P P m F F F m F F F m Μ Μ Μ F F F m d d d d d d v v v v v v m m m m m m m x x x S S S m y R R Μ R m
273 d v m = m x + E + y = x ( =,,, ) ( 9) = P + F + = = R Q(,,, m) (0) = m = e p = = E S P x f = F S =,,, =,, m =,,, m =,,, ( ) ( ) (, =,,, m) (3) a a a a a a A = Μ Μ Μ Μ a a a
274 e e e m e e e m E = Μ Μ Μ Μ e e e m p p p p p p P = Μ Μ Μ Μ p p p m m m f f fm f f f m F = Μ Μ Μ Μ f f f m m mm a 0 0 a a 0 0 = ( 7) Μ Μ Μ Μ 0 0 S = aq a m I A Ea X Y P I Fa Q R ( 8) X Q = I - A - Ea (9) Y - P I - Fa R Q = Q - aq = (I - a)q (0)
275 = x + d + v + m = x ( =,,, ) ( ) m ( + ) x + a P + d + v + m = = = ( + ) x ( =,,, ) ( ) = m x + a P = x ( =,,, ) = m a + a P = ( =,,, ) = = A T + P a =, (3) m ρ ( + ) E + a F + d + v + m = = T = S ( = m) (4) h m d + v + m = e + ( =,,, m) S = e + a f + h = ( =,,, m) = = T T E + F a + H = ( 5) T T = A P a + O ( 6) T T E F a H
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