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K E N Z U 01 7 16 HP M. 1

1 4 1.1 3.......................... 4 1.................................... 4 1..1..................................... 4 1...................................... 5................................ 5.................................. 6 1.3........................ 8 1.3.1............................ 8 1.3.................................. 8 1.3.3................................ 9 1.3.4........................ 9 1.3.5........................... 11................................ 11 1.4.............................. 13 1.4.1....................... 14 1.4......................... 15............................ 17 19.1............................... 19..................................... 19..1................................3.................................... 3.3.1.................................. 3.3........................... 4.3.3........................... 5.3.4....................... 6.3.5................................ 6.4................................. 7........................... 9.5........................... 30.5.1............................ 30.......................... 3................................ 33.5............................ 33.6......................................... 36.7........................... 38........................... 38

................................ 39................................ 39............................ 39................................. 40................................ 40................................ 41 3 43 3.1...................................... 43 3.1.1................................... 43............................. 44 3.1. 4 ( )...................... 47....................... 47 3.1.3............................ 5............................... 53 3...................................... 53 3..1..................................... 53 3.......................... 55............................... 55.................................. 56.................................. 56 3..3............................. 58....................... 59 3..4.......................... 60.................................... 60................................ 6 4 63 4.1........................ 63 4.1.1........................ 63 4.1. 4........... 65 4.1.3 4.......................... 66 4.1.4................................ 67 4.1.5........... 69 4.1.6.................................. 7....................... 7 4................................ 73 4..1................................. 73 4............................ 75 4.3............................. 76 4.3.1.......................... 76 4.3...................... 77 3

1 1.1 3 1 1 3 3 1. 1..1 1 1 1 1 1 S 1 S 1 S S S 1 z S z S V t 0 y y V 4

1 S S V S t (t) = (t) V t (1..1) d (t) dt = d(t) dt V (1..) S 1 S V S S S S 1 (1..) t d (t) dt = d (t) dt (1..3) S, S V S m d (t) dt = f (1..4) f S S f f = f (1..3) m d (t) dt = f (1..5) S (1..4) S S 1.. S S S (1..) V (1..) t d dt = d dt dv dt a = a A (1..6) S 1 S S S m ma = ma ma S ma = f ma (1..7) 3 5

f = f S f ma S S f = 0 (1..7) ma = ma S A S f = ma f 3 ( A θ S A S T θ T sin θ mg A S ma T mg θ 4 S A T m d = ma = T sin θ (1..8) dt 0 m d = 0 = T sin θ ma (1..9) dt ma A S z ω t = 0 S, S P t S, S, = cos ωt y sin ωt y = sin ωt + y cos ωt (1..10) S P f P S mẍ = f mÿ = f y (1..11) 5 (1..10) ẍ = (ẍ ωy ω ) cos ωt (ÿ + ωẋ y ω ) sin ωt ÿ = (ẍ ω y ω ) sin ωt + (ÿ + ωẋ y ω ) cos ωt (1..1) 3 4 5 f S S 6

(1..11), (1..1) f = A cos ωt B sin ωt f y = A sin ωt + B cos ωt A = m(ẍ ω y ω ) B = m(ÿ + ωẋ y ω ) (1..13) A = f cos ωt + f y sin ωt B = f sin ωt + f y cos ωt (1..14) f, y f = f cos ωt + f y sin ωt f y = f sin ωt + f y cos ωt (1..15) (1..14), (1..15) S P P S (1..11) S (1..16) S f f y mω, mω y ω y, ωẋ m ẍ = f + mω + mωy mÿ = f y + mω y mωẋ (1..16) ω z ω z 0 v 0 f 0 o f 0 c ω = (0, 0, ω) (1..17) = (, y ), v = (ẋ, y ) f c f o y f c = mω f o = mv ω (1..18) 6 v S m=1 P f = 1 P S (1..16) «6 a a 3 a b = b b 3, a3 a1 b 3 b 1, a1 a b 1 b y f = 1 ω = v 0 = 10t = 10 S P y y ωt ωt P y S 7

(1..16) f = 0, f y = 0 m ẍ = cos ωt + ω + ωy mÿ = sin ωt + ω y ωẋ Mathematica ω = v 0 = 10 t = 10 P S P 1.3 1.3.1 7 1.3. (1..1) 8 S, S, t S S t t S z V t y S z 0 t = t (1.3.1) y V = V t t = t (1.3.) 9 S v V (1..) v = v V (1.3.3) 7 8 1 9 8

(1.3.3) 0 = t, 1 =, = y, 3 = z, V = (V 1, V, V 3 ) 0 1 3 1 0 0 0 = V 1 1 0 0 V 0 1 0 V 3 0 0 1 0 1 3 µ = G µν V 4 G µν ν (1.3.4) ν=0 1.3.3 1. G A B C C G C = AB. G A AE = EA = A E G E 3. G A AA 1 = A 1 A = E A 1 G 4. 3 ABC A(BC) = (AB)C = ABC (1.3.) G(V ) G(V ) : = V t, t = t (1.3.5) G(V ) : = V t, t = t, t t t G(V )G(V ) G(V + V ) = ( V t) V t = (V + V )t, t = t (1.3.6) G(V )G(V ) = G(V + V ) (1.3.7) 1 10 11 G(0) G(V ) G( V ) 1 1.3.4 t v = vt + 0 13 10 G(V )(G(V )G(V )) = G(V )G(V + V ) = G(V + V + V ), etc 11 1 G(V )G( V ) = G( V )G(V ) = G(0) t v =tan α α 0 P 13 = 1 gt + v 0t + 0 9

= V t t = t (1.3.8) (, t) = (0, 0) t = 0 (1.3.8) = t = 0 t = (1/V ) (t, ) 1/V t t t φ t φ V : φ π/) p p, tan φ = ( p p)/t p,... p = p t p tan φ = p V t p (1.3.10) 1 tp = t p cos φ t p = V = tan φ (1.3.9) t p cos φ = t p 1 + tan φ = 1 + V t p (1.3.11) (1.3.8) 1 + V t t p 1 + V cos φ = A B = t p t p t p A t t φ φ t p B t t 1 + V = t p cos φ,... t 1 + V p = t p (1.3.1) t t t t 1 + V P S v P S V S P P Q sin(α φ) = Q sin(π/ α)... Q sin(α φ) = P Q cos α = Q cos α = tan α cos φ sin φ = cos φ(tan α tan φ) = Q = p, P Q = 1 + V t p t p v V 1 + V p φ p P P, Q P Q = 1 p 1 + V t p = v 1 + V,... v = v V 10

t tan α = v P t φ t 1 + V tan φ = V P α α α φ π/ α Q, 1.3.5 1 1 v ϕ(, t) = A cos(k ωt), (k = π/λ, ω = πν, T = π/ω) (1.3.13) k, ω ν T λ v = λν t = 0 = 0 t 1 = π/ω = 0 V V < v π/ω=1/ν A n A = n 1 ν = n ν (1.3.14) B A t 5 t 4 t 3 t t 1 t α t t 1 + V B λ v = λ 1/ν = tan α ν t A tan 1 v B tan 1 V λ v (tan 1 v tan 1 V ) B = n ν 1 + V (1.3.15) 11

... B sin AB = A B = sin BA sin AB A sin BA = sin(tan 1 v) cos(tan 1 V ) cos(tan 1 v) sin(tan 1 V )) sin(tan 1 v) sin α cos β cos α sin β = sin α = v V 1 v 1 + V (1.3.16) tan 1 v = α cos α = tan 1 V = β cos β = 1, sin α = v 1 + v 1 + v 1, sin β = V 1 + V 1 + V (1.3.16) (1.3.14) (1.3.15) A/B = ν ν 1 1 + V (1.3.16) ν ν = v V v = 1 V v < 1 (1.3.17) V t 1/V t α t 1 + V B B β tan 1 v = α tan 1 V = β A C β A α (π α β) C ν BC = n ν 1 + V (1.3.18) AB BC = sin(α + β) sin α = sin α cos β + cos α sin β sin α = v + V v 1 1 + V (1.3.19) AB = n/ν AB/BC = (n/ν ) 1 + V (1.3.19) ν ν = v + V v = 1 + V v > 1 (1.3.0) 1

1.4 v ρ(, t) ( + y + z 1 ) v t ρ(, t) = 0 (1.4.1) v v V v) S (1.4.1) 1 = V t, t = t = t = t t + t t + t t = = t V 1 14 ( + V v V (1.4.) ρ(, t) v t 1 ) v V t ρ(, t ) = 0 (1.4.3) (1.4.1) V ( ) V E(, t) = 1 ε 0 B(, t) E(, t) = t B(, t) = 0 B(, t) = µ 0 J(, t) + 1 E(, t) c t E B ( + y + z 1 ) c t E(, t) = 0 ( + y + z 1 ) c t B(, t) = 0 (1.4.4) (1.4.5) ( ) 15 c 14 15 13

V (1.4.3) v = c V V v +V v V 16 c + V c V 17 V 1.4.1 1887 V V B L M V B B M A L c + V M M C L c V M A B B A M C A B l A t 1 c + V c V t 1 = l c + V + l c V = C l/c 1 β, β = V c V l ct / ct / V t (1.4.6) B B B t ( ) 1 ( ) 1 ct = l + V t,... t = l c V = l/c 1 β (1.4.7) L β 1 18 ( ) 1 = c(t t 1 ) = l 1 1 β 1 β lβ (1.4.8) V 1 β 16 V, V 17 0.5km/s 30km/s 18 c 3 10 10 cm/sec V V 3 10 6 cm/sec 14

A l/ 1 β t 1 = (l/c)/ 1 β t 1 = t 19 M E M 1 (1.4.4) (S ) V (S ) S S B = µ 0 J + 1 E c t 1 (V E) c E = B t + (V B) B = 0, E = 1 ε 0 ρ (1.4.9) 1.4. 1 0 ( 1 ) ( c t φ(, t) = 0 u 1 ) c w φ(u, w) = 0 (1.4.10) (, t) (u, w) u = A 1 ( ) ( ) ( ) u = A + Bt u A B = w = C + Dt v C D t (1.4.11) = A 1 u, (A 1 0) ( ) A 1 = 1 D B A B, = = AD BC 0 C A C D ( ) ( ) ( ) (1.4.1)... = 1 D B u t C A w = (u, w), t = t(u, w) = u u + w w = A u + C w t = u t u + w t w = B u + D (1.4.13) w 19 A 0 3 1 15

(1.4.10) ( 1 ) c t φ(, t) ) = (A B c u ( D c C ) 1 c w + A B /c = 1 D c C = 1 AC BD/c = 0 ( AC BD ) c u A, B, C, D (1.4.14) w (1.4.14) (1.4.15) 1 c t u 1 c w (1.4.16) (u, w) A, B, C, D (1.4.15) 4 3 1 1 A B, C, D 1 B = c A 1, C = 1 c A 1, D = A (1.4.17) χ A = cosh χ B = c sinh χ, C = 1 sinh χ, D = cosh χ (1.4.18) c B, C, D (1.4.11) u = cosh χ ct sinh χ w = t cosh χ c sinh χ (χ ) (1.4.19) 3 cosh χ = cos(iχ) = eχ + e χ sinh χ = i sin(iχ) (1.4.0) (1.4.19) u = cos(iχ) + ict sin(iχ) icw = sin(iχ) + ict cos(iχ) ( ) ( u cos θ = icw sin θ ) ( ) sin θ cos θ ict (1.4.1) θ = iχ ict iχ (1.4.1) u + (icw) = ( cos θ + ict sin θ) + ( sin θ + ict cos θ) = + (ict) (1.4.) ict icw ict iχ icw u iχ u( ) cosh sinh = 1 3 cosh θ = (e θ + e θ )/, sinh θ = (e θ e θ )/, cos θ = (e iθ + e iθ )/, sin θ = (e iθ e iθ )/i 16

+ (ict) ict iχ + (ict) 3, y, z, ict 4 ict iχ = cos θ + 0 sin θ y = y z = z (1.4.3) ict = sin θ + ict cos θ ict cos θ sin θ 0 0 ict y = sin θ cos θ 0 0, θ = iχ (1.4.4) 0 0 1 0 y z 0 0 0 1 z (ict ) + + y + z = (ict) + + y + z (1.4.5) iχ cosh χ 1 sinh χ χ (1.4.6) (1.4.19) u = ctχ w = t c χ (1.4.7) χ = V/c (1.4.8) u = V t w = t V c = V t t = t (1.4.8) u w t c (1.4.8) 4 u w t 1. (t) = (t) V t, t = t. v = v V 17

3. ( + y + z 1 ) c t φ(, t) = 0 (1.4.9) V (1.4.9) 1 ( + V c V c t 1 ) c V t φ(, t ) = 0 (1.4.30) 4. V 5. V 1 β 6. (1.4.9) ict iχ 7. 18

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