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- しょうこ みうら
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1 2.,, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 4
2 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 5
3 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 6
4 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 7
5 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 8
6 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 9
7 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 10
8 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 11
9 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 12
10 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 13
11 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 14
12 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 15
13 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 16
14 ,,. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 17
15 :,,,,,,,.,. SEM, AFM, SAM,,,, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 18
16 :,,,,,,,, :,,, :,,, :,, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 19
17 ( ),.,... g o + e o = f(x, n) (1) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 20
18 , Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 21
19 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 22
20 , span, dynamic range accuracy Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 23
21 N l = 1 N S 2 = 1 N 1 : N l i (2) i=1 N (l i l) 2 (3) i=1 systematic error accidental error Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 24
22 ,, 2. y = f 1 (x 0 +Δx, Δe) f 2 (x 0 +Δx, Δe) (4) f 1 (x 0, 0) = f 2 (x 0, 0) (5) f 1 x = f 2 x=x0,e=0 x (6) x=x0,e=0 f 1 e = f 2 x=x0,e=0 e (7) x=x0,e=0 (8) y 2 f x Δx +2 2 f ΔxΔe (9) x e, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 25
23 : : : Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 26
24 3.,, m : : P 10 5d : :,. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 27
25 2 θ 2 dm L L = d (10) tan θ 2 Δd θ L +ΔL = d tan θ + Δd (11) tan θ θ Δθ θ. d L +ΔL = (12) tan(θ +Δθ) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 28
26 , Δt L = cδt (13) 2. 1mm (1mm) = cδt 2 Δt 6ps , Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 29
27 . f Λ Λ= c f (14) φ L L = 1 2 (N + φ )Λ (15) 2π L>Λ/2 Λ > 2L. L = φ Λ 4π (16) N = 1 2π (Λ Λ φ φ) (17) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 30
28 A cos 2πft K cos 2πf L t = 1 2 AK[cos 2π(f +f L)t+cos2π(f f L )t] (18) B cos(2πft + φ) K cos 2πf L t = 1 2 BK[cos(2π(f + f L)t + φ)+cos(2π(f f L )t + φ)] (19), f f L 1 2 AK cos 2π(f f 1 L)t 2 BK cos(2π(f f L)t + φ) (20) φ. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 31
29 :. λ, L 1, L 2 I = A + B cos 2π(L 1 L 2 ) (21) λ, 1/10 (50nm). Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 32
30 GPS:,. VLBI:...( ) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 33
31 , (km) ( ) (m) (nm, μm, mm) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 34
32 :,,,,,,.,,. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 35
33 . (a) 1. h 2. θ (b) θ δ a = h tan θ hθ (22) δ b =(L d)(1 cos θ) L d θ 2 (23) 2 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 36
34 N, N 1 N. : K N 1 + x. 0 <x< 1/N. M (M 1)/N = x + M(N 1)/N 2 (24). x = M/N 2. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 37
35 :,. :.. : p θ a = θ p (25) 2π.( ) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 38
36 ,,., ( ),.,. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 39
37 :,. : x, θ θ = x (26) a L 2θ d =2θ L =2 x a L = 2L a x (27) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 40
38 4.,,,,.,,. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 41
39 ,. r(θ) R = V E (28), Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 42
40 C = ɛs d (29) C (F), d (m), S (m 2 ), ɛ (F/m) Δd Δd C 1 = ɛs d +Δd, C 2 = ɛs d Δd (30), ΔV = V 1 V 2 = V d Δd (31). Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 43
41 ( 1). ( ),,,. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 44
42 ( 2) A B 1/4 B UP (1) (2) A (1) (2) (3) (4) (6) (3) DOWN (4) (5) (5) UP (7) (6) (7) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 45
43 0 1 X 2 X 3 XX X XXXXXXX 128 X 129 X X. 252 XXXXXX 253 XXXXXX X 254 XXXXXXX 255 XXXXXXXX Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 46
44 ,. v(m/s). x p x A y p y B. A T A, B T B. x v x T A y v y T B T x = p x /v x, T y = p y /v y (32) v =(p x /T x p y /T y ) T. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 47
45 ( 1) L 2, 2 x v., f(x)(, ).. A(x =0) B(x = L).. f A (t) =f(0 vt), f B (t) =f(l vt) (33) f(x). φ ff (x) = lim X 1 2X X X f(χ)f(χ + x)dχ (34) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 48
46 ( 2) f A (t) f B (t). φ AB (t) = lim T 1 2T T T f A (τ)f B (τ + t)dτ (35) f A (t) =f(0 vt) f B (t) =f(l vt). φ AB (t) = lim T 1 2T T T f( vτ))f(l v(τ + t))dτ = φ ff (L vt) (36) φ ff (x) x =0. φ ff (L vt) t 0 v = L/t 0. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 49
47 seismic pick up ( ). m k, c.. x a. m d2 x dt 2 + cdx dt m + kx = ma (37) d 2 x dt 2 + c dx m dt + k x = a (38) m Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 50
48 seismic pick up ( ). d 2 x dt 2 + c dx m dt + k x =0 (39) m (39) Ce γt (39).. γ 2 + c m γ + k m γ. γ = 1 2 ( c m ± c 2 =0 (40) m 2 4k m ) (41) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 51
49 seismic pick up ( ) (39) C 1 exp( 1 2 ( c m + c 2 m 2 4k m )t)+c 2 exp( 1 2 ( c m c 2 m 2 4k m )t). (42) ω n = k/m, ζ = c/2 mk C 1 exp( ζω n t+ ωn(ζ 2 2 1)t)+C 2 exp( ζω n t ωn(ζ 2 2 1)t) (43). ζ 2 < 1. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 52
50 seismic pick up ( 4) g(t). d 2 (g(t) a(t)) dt 2 +2ζω n d(g(t) a(t)) dt + ω 2 n(g(t) a(t)) = a(t) (44) t<=0 g(t) =0,. s 2 G(s)A(s)+2ζω n sg(s)a(s)+ω 2 ng(s)a(s) = A(s) (45) G(s) g(t). d 2 g(t) dt 2 s 2 G(s), dg(t) dt sg(s), g(t) a(t) G(s)A(s). Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 53
51 seismic pick up ( ) G(s) G(s) = 1 s 2 +2ζω n s + ω 2 n (46) s = jω ω. 1 G(jw)= (jw) 2 +2ζω n (jw)+ωn 2 (47) G(jw), arctan(im(g(jw))/re(g(jw))). G(jw) = x(t) a(t) = (1/ω 2 n) (1 (ω/ωn ) 2 ) 2 +(2ζω/ω n ) 2 (48) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 54
52 -.,. R = ρl/a(a, ρ ) ΔR R = Δρ ρ + Δl l ΔA A (49) K =( ΔR R )( l Δl )=1+(Δρ ρ )( l Δl ) (ΔA A )( l Δl ) (50) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 55
53 ( 1) R 2 : R 1 = R 3 : R 4, R Δe = E( 3 +ΔR 3 R 2 +ΔR 2 ) R 3 +ΔR 3 + R 4 +ΔR 4 R 1 +ΔR 1 + R 2 +ΔR 2 = E (R 3 +ΔR 3 )(R 1 +ΔR 1 ) (R 2 +ΔR 2 )(R 4 +ΔR 4 ) (R 1 +ΔR 1 + R 2 +ΔR 2 )(R 3 +ΔR 3 + R 4 +ΔR 4 ) 1 (R 2+ΔR 2 )(R 4 +ΔR 4 ) (R 1 +ΔR 1 )(R 3 +ΔR 3 ) = E = E (1 + R 2+ΔR 2 R 1 +ΔR 1 )(1 + R 4+ΔR 4 R 3 +ΔR 3 ) 1 R 2+ΔR 2 R 1 +ΔR 1 R 4 +ΔR 4 R 3 +ΔR 3 (1 + R 2+ΔR 2 R 1 +ΔR )(1 + R 4+ΔR 4 1 R 3 +ΔR ) = E 3 (1+ΔR 4 /R 4 ) (1+ΔR 1 /R 1 )(1+ΔR 3 /R 3 ) 1 (1+ΔR 2/R 2 ) (1 + R 2+ΔR 2 R 1 +ΔR 1 )(1 + R 4+ΔR 4 R 3 +ΔR 3 ) (51) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 56
54 ( 2) Δe E 1 (1 + α)(1 + 1/α) (ΔR 1 R 1 ΔR 2 R 2 + ΔR 3 R 3 ΔR 4 R 4 ) R 1 =R 2 =R 3 =R 4, ΔR 1 =ΔR 2 =ΔR 4 =0 (52) Δe = 1 4 (ΔR 3 R 3 )E (53) Δe = 1 4 K(Δl )E (54) l Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 57
55 ..., α Δe E (1 + α) 2(((ΔR 3 ) R T ( ΔR 4 ) 3 R T +( ΔR 3 ) ɛ ) (55) 4 R 3 α Δe E (1 + α) 2(ΔR 3 ) ɛ (56) R 3. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 58
56 ,. ΔR A = ΔR C = ΔR R A R C R (57) ΔR B = ΔR D = ν ΔR (58) R B R D R ν. Δe E 1 4 (ΔR R + νδr R + ΔR R + νδr R )=1 Kɛ(1 + ν)e (59) 2 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 59
57 /, θ = 32L πd 4 G T (60) L, d, G P = 2πn 60 T (61) n. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 60
58 5. ( ) ( ) ( ) ( ) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 61
59 6. p, v p 0 = p ρv2 (62). p, 1 2 ρv2 p 0, 2(p v = 0 p) ρ. (63). Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 62
60 i 2 R w (T w T )(a + bv n dt w )=C w dt i R w. (64) R w i, i. dt w dt =0 C w,.. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 63
61 ( ) 2 2θ. 2, 2λ n / sin θ. λ n. v y f = v/(2λ n / sin θ).,. θ θ v Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 64
62 ( ).. (, ). p ρv2 1 = p ρv2 2 (65) (, ) S 1,S 2 Q = S 1 v 1 = S 2 v 2, S Q = 2 2(p 1 p 2 ) 1 (S2 /S 1 ) 2 (66) ρ Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 65
63 ..,. E v =( D/2 0 E = BD v 2πrv(r)dr)/(πr 2 ) (67) Q = v πd 2 /4=E (πd)/(4b) v B Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 66
64 .,. f = S v (68) d. S 0.2.,., Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 67
65 ,,,.,. ( ). Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 68
66 :., : :,,, :,,,,. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 69
67 ,.. ΔI/I =(F 2 /a)dc(ρ/ρ 0 ) dρ (69) dρ Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 70
68 . ΔD = C(ρ ρ 0 )D (70),. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 71
69 7..,,,. 1993,ISO. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 72
70 (accuracy) precesion( ) dispersion( ) type A uncertainty( certainty( standard un- ) ) trueness( ) bias( ) Type B uncertainty( ) combined standard uncertainty( ) exonded uncertainty ( ) A. B. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 73
71 ( 1). x 1, x 2, y 0. y 0 = x 1 + x 2 (71) n e 1n, e 2n n e 0n = e 1n + e 2n (72). N 1 N e 2 N 1 0n = 1 N e 2 N 1 1n + 1 N N 1 n=1 n=1 n=1 e 1n e 2n + 1 N 1 N n=1 e 2 2n (73) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 74
72 ( 2) x 1 x 2 N e 1n e 2n =0 (74). n=1 N 1 N e 2 N 1 0n = 1 N e 2 N 1 1n + 1 N 1 n=1 n=1 N n=1 e 2 2n (75) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 75
73 ( 3) y 0, x 1, x 2 S 0, S 1, S 2. S 2 0 = S2 1 + S2 2 (76) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 76
74 ( 4) y 0 = a 1 x 1 + a 2 x a m x m (77) S y0 = a 2 1 S2 a1 + a2 2 S2 a2 + + a2 ms 2 am (78) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 77
75 ( 5) y 0, x. y = Ax (79). y = Ax + n (80) Σ nn,,,, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 78
76 ... Σ nn = = lim N = lim N lim N 1 N 1 1 N 1 1 N n n n T n (81) N 1 n=1 n 1n N n 2n. ( n 1 n 2 n M ) (82) n=1 n Mn Nn=1 n 1n n 1n Nn=1 n 1n n Mn..... Nn=1 (83) n Mn n 1n Nn=1 n Mn n Mn Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 79
77 . lim N = lim N =Σ nn 1 N 1 N (y n Ax n )(y n Ax n ) T (84) n=1 1 N 1 N n n n T n (85) n=1 (86) a m, (m =1, 2,...,M) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 80
78 A x ˆx. ˆx = A 1 y = A 1 (Ax + n) (87) ˆx. lim N = lim N 1 N 1 N (ˆx n x n )(ˆx n x n ) T (88) n=1 1 N 1 = A 1 ( lim N N (A 1 n n )(A 1 n n ) T (89) n=1 1 N 1 N n n n T n )(A 1 ) T = A 1 S nn (A 1 ) T (90) n=1 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 81
79 2 N : l i, i =1, 2,..., N N (l i X) (91) l=1 ˆX ˆX, (BLUE=Best Linear Unbiased Estimate).. X = 1 N N l i (92) l=1 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 82
80 2 ( ),. y, x, e x. y = f(x, e) (93),. f(x, e) ax 2 + bx + c + e (94),. r i = y i (ax 2 i + bx i + c + e i ) (95) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 83
81 2 ( 2), e i r i r i = y i (ax 2 i + bx i + c) (96) N N Q = ri 2 = N yi 2 2 y i (ax 2 i + bx i + c)+ i=0 i=0 i=0 â, ˆb, ĉ N (ax 2 i + bx i + c) 2 i=0 (97) 2 Q Q a =0, Q b =0, Q =0 (98) c Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 84
82 2 ( 3) Q a = 2 N i=0 y i x 2 i + N a ( (a 2 x 4 i + b2 x 2 i + c2 +2abx 3 i +2bcx i +2cax 2 i )) = 2 i=0 N y i x 2 N i +2 (ax 4 i + bx3 i + cx2 i ) (99) i=0 Q b = 2 N i=0 Q c = 2 N i=0 y i x i +2 y i +2 i=0 N (ax 3 i + bx2 i + cx i) (100) i=0 N (ax 2 i + bx2 i i=0 + c) (101) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 85
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微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)
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II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka )
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13 13.1 O r F R = m d 2 r dt 2 m r m = F = m r M M d2 R dt 2 = m d 2 r dt 2 = F = F (13.1) F O L = r p = m r ṙ dl dt = m ṙ ṙ + m r r = r (m r ) = r F N. (13.2) N N = R F 13.2 O ˆn ω L O r u u = ω r 1 1:
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r(t) t r(t) O v(t) = dr(t) dt a(t) = dv(t) dt = d2 r(t) dt 2 r(t), v(t), a(t) t dr(t) dt r(t) =(x(t),y(t),z(t)) = d 2 r(t) dt 2 = ( dx(t) dt ( d 2 x(t) dt 2, dy(t), dz(t) dt dt ), d2 y(t) dt 2, d2 z(t)
f(x) = f(x ) + α(x)(x x ) α(x) x = x. x = f (y), x = f (y ) y = f f (y) = f f (y ) + α(f (y))(f (y) f (y )) f (y) = f (y ) + α(f (y)) (y y ) ( (2) ) f
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59 7 7.1 σ-ω σ-ω σ ω σ = σ(r), ω µ = δ µ,0 ω(r) (6-4) (iγ µ µ m U(r) γ 0 V (r))ψ(x) = 0 (7-1) U(r) = g σ σ(r), V (r) = g ω ω(r) σ(r) ω(r) (6-3) ( 2 + m 2 σ)σ(r) = g σ ψψ (7-2) ( 2 + m 2 ω)ω(r) = g ω ψγ
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m dv = mg + kv2 dt m dv dt = mg k v v m dv dt = mg + kv2 α = mg k v = α 1 e rt 1 + e rt m dv dt = mg + kv2 dv mg + kv 2 = dt m dv α 2 + v 2 = k m dt d
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