KENZOU

Similar documents
1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2


x,, z v = (, b, c) v v 2 + b 2 + c 2 x,, z 1 i = (1, 0, 0), j = (0, 1, 0), k = (0, 0, 1) v 1 = ( 1, b 1, c 1 ), v 2 = ( 2, b 2, c 2 ) v


18 2 F 12 r 2 r 1 (3) Coulomb km Coulomb M = kg F G = ( ) ( ) ( ) 2 = [N]. Coulomb

曲面のパラメタ表示と接線ベクトル

Gmech08.dvi

1. z dr er r sinθ dϕ eϕ r dθ eθ dr θ dr dθ r x 0 ϕ r sinθ dϕ r sinθ dϕ y dr dr er r dθ eθ r sinθ dϕ eϕ 2. (r, θ, φ) 2 dr 1 h r dr 1 e r h θ dθ 1 e θ h

(1) D = [0, 1] [1, 2], (2x y)dxdy = D = = (2) D = [1, 2] [2, 3], (x 2 y + y 2 )dxdy = D = = (3) D = [0, 1] [ 1, 2], 1 {

08-Note2-web

() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)

Gmech08.dvi

Untitled

( ) ( )

n=1 1 n 2 = π = π f(z) f(z) 2 f(z) = u(z) + iv(z) *1 f (z) u(x, y), v(x, y) f(z) f (z) = f/ x u x = v y, u y = v x

2 1 κ c(t) = (x(t), y(t)) ( ) det(c (t), c x (t)) = det (t) x (t) y (t) y = x (t)y (t) x (t)y (t), (t) c (t) = (x (t)) 2 + (y (t)) 2. c (t) =

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x

II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka )

m d2 x = kx αẋ α > 0 (3.5 dt2 ( de dt = d dt ( 1 2 mẋ kx2 = mẍẋ + kxẋ = (mẍ + kxẋ = αẋẋ = αẋ 2 < 0 (3.6 Joule Joule 1843 Joule ( A B (> A ( 3-2

meiji_resume_1.PDF

( ) sin 1 x, cos 1 x, tan 1 x sin x, cos x, tan x, arcsin x, arccos x, arctan x. π 2 sin 1 x π 2, 0 cos 1 x π, π 2 < tan 1 x < π 2 1 (1) (


A (1) = 4 A( 1, 4) 1 A 4 () = tan A(0, 0) π A π

d (K + U) = v [ma F(r)] = (2.4.4) t = t r(t ) = r t 1 r(t 1 ) = r 1 U(r 1 ) U(r ) = t1 t du t1 = t F(r(t)) dr(t) r1 = F dr (2.4.5) r F 2 F ( F) r A r

Z: Q: R: C: sin 6 5 ζ a, b

mugensho.dvi


ma22-9 u ( v w) = u v w sin θê = v w sin θ u cos φ = = 2.3 ( a b) ( c d) = ( a c)( b d) ( a d)( b c) ( a b) ( c d) = (a 2 b 3 a 3 b 2 )(c 2 d 3 c 3 d

Note.tex 2008/09/19( )

i 18 2H 2 + O 2 2H 2 + ( ) 3K

2 0.1 Introduction NMR 70% 1/2

Gmech08.dvi

2 1 x 1.1: v mg x (t) = v(t) mv (t) = mg 0 x(0) = x 0 v(0) = v 0 x(t) = x 0 + v 0 t 1 2 gt2 v(t) = v 0 gt t x = x 0 + v2 0 2g v2 2g 1.1 (x, v) θ

応力とひずみ.ppt

(3) (2),,. ( 20) ( s200103) 0.7 x C,, x 2 + y 2 + ax = 0 a.. D,. D, y C, C (x, y) (y 0) C m. (2) D y = y(x) (x ± y 0), (x, y) D, m, m = 1., D. (x 2 y

c y /2 ddy = = 2π sin θ /2 dθd /2 [ ] 2π cos θ d = log 2 + a 2 d = log 2 + a 2 = log 2 + a a 2 d d + 2 = l

.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =,

(Bessel) (Legendre).. (Hankel). (Laplace) V = (x, y, z) n (r, θ, ϕ) r n f n (θ, ϕ). f n (θ, ϕ) n f n (θ, ϕ) z = cos θ z θ ϕ n ν. P ν (z), Q ν (z) (Fou

1 12 ( )150 ( ( ) ) x M x 0 1 M 2 5x 2 + 4x + 3 x 2 1 M x M 2 1 M x (x + 1) 2 (1) x 2 + x + 1 M (2) 1 3 M (3) x 4 +

5 1.2, 2, d a V a = M (1.2.1), M, a,,,,, Ω, V a V, V a = V + Ω r. (1.2.2), r i 1, i 2, i 3, i 1, i 2, i 3, A 2, A = 3 A n i n = n=1 da = 3 = n=1 3 n=1

Fubini

I ( ) 2019

( 4) ( ) (Poincaré) (Poincaré disk) 1 2 (hyperboloid) [1] [2, 3, 4] 1 [1] 1 y = 0 L (hyperboloid) K (Klein disk) J (hemisphere) I (P

S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt

1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0

A

dynamics-solution2.dvi

y π π O π x 9 s94.5 y dy dx. y = x + 3 y = x logx + 9 s9.6 z z x, z y. z = xy + y 3 z = sinx y 9 s x dx π x cos xdx 9 s93.8 a, fx = e x ax,. a =

F S S S S S S S 32 S S S 32: S S rot F ds = F d l (63) S S S 0 F rot F ds = 0 S (63) S rot F S S S S S rot F F (63)

) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8)

untitled

Kroneher Levi-Civita 1 i = j δ i j = i j 1 if i jk is an even permutation of 1,2,3. ε i jk = 1 if i jk is an odd permutation of 1,2,3. otherwise. 3 4

() (, y) E(, y) () E(, y) (3) q ( ) () E(, y) = k q q (, y) () E(, y) = k r r (3).3 [.7 ] f y = f y () f(, y) = y () f(, y) = tan y y ( ) () f y = f y

sec13.dvi

M3 x y f(x, y) (= x) (= y) x + y f(x, y) = x + y + *. f(x, y) π y f(x, y) x f(x + x, y) f(x, y) lim x x () f(x,y) x 3 -

II ( ) (7/31) II ( [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Re

chap03.dvi


S I. dy fx x fx y fx + C 3 C dy fx 4 x, y dy v C xt y C v e kt k > xt yt gt [ v dt dt v e kt xt v e kt + C k x v + C C k xt v k 3 r r + dr e kt S dt d

I 1

Korteweg-de Vries

C : q i (t) C : q i (t) q i (t) q i(t) q i(t) q i (t)+δq i (t) (2) δq i (t) δq i (t) C, C δq i (t 0 )0, δq i (t 1 ) 0 (3) δs S[C ] S[C] t1 t 0 t1 t 0

0 = m 2p 1 p = 1/2 p y = 1 m = 1 2 d ( + 1)2 d ( + 1) 2 = d d ( + 1)2 = = 2( + 1) 2 g() 2 f() f() = [g()] 2 = g()g() f f () = [g()g()]

K E N Z OU

TOP URL 1

lim lim lim lim 0 0 d lim 5. d 0 d d d d d d 0 0 lim lim 0 d

1 1 sin cos P (primary) S (secondly) 2 P S A sin(ω2πt + α) A ω 1 ω α V T m T m 1 100Hz m 2 36km 500Hz. 36km 1

Introduction to Numerical Analysis of Differential Equations Naoya Enomoto (Kyoto.univ.Dept.Science(math))

ψ(, v = u + v = (5.1 u = ψ, v = ψ (5.2 ψ 2 P P F ig.23 ds d d n P flow v : d/ds = (d/ds, d/ds 9 n=(d/ds, d/ds ds 2 = d 2 d v n P ψ( ψ

B 38 1 (x, y), (x, y, z) (x 1, x 2 ) (x 1, x 2, x 3 ) 2 : x 2 + y 2 = 1. (parameter) x = cos t, y = sin t. y = f(x) r(t) = (x(t), y(t), z(t)), a t b.

t (x(t), y(t)), a t b (x(a), y(a)) t ( ) ( ) dy s + dt dt dt [a, b] a a t < t 1 < < t n b {(x(t i ), y(t i ))} n i ( s(t) ds ) ( ) dy dt + dt dt ( ) d

1 1. x 1 (1) x 2 + 2x + 5 dx d dx (x2 + 2x + 5) = 2(x + 1) x 1 x 2 + 2x + 5 = x + 1 x 2 + 2x x 2 + 2x + 5 y = x 2 + 2x + 5 dy = 2(x + 1)dx x + 1


,,,17,,, ( ),, E Q [S T F t ] < S t, t [, T ],,,,,,,,

1 I 1.1 ± e = = - = C C MKSA [m], [Kg] [s] [A] 1C 1A 1 MKSA 1C 1C +q q +q q 1

I A A441 : April 21, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) Google

b3e2003.dvi

l µ l µ l 0 (1, x r, y r, z r ) 1 r (1, x r, y r, z r ) l µ g µν η µν 2ml µ l ν 1 2m r 2mx r 2 2my r 2 2mz r 2 2mx r 2 1 2mx2 2mxy 2mxz 2my r 2mz 2 r

,. Black-Scholes u t t, x c u 0 t, x x u t t, x c u t, x x u t t, x + σ x u t, x + rx ut, x rux, t 0 x x,,.,. Step 3, 7,,, Step 6., Step 4,. Step 5,,.


No δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i x j δx j (5) δs 2

2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP


高等学校学習指導要領

高等学校学習指導要領


重力方向に基づくコントローラの向き決定方法

( ) ,

ver F = i f i m r = F r = 0 F = 0 X = Y = Z = 0 (1) δr = (δx, δy, δz) F δw δw = F δr = Xδx + Y δy + Zδz = 0 (2) δr (2) 1 (1) (2 n (X i δx

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.

x (x, ) x y (, y) iy x y z = x + iy (x, y) (r, θ) r = x + y, θ = tan ( y ), π < θ π x r = z, θ = arg z z = x + iy = r cos θ + ir sin θ = r(cos θ + i s

構造と連続体の力学基礎

i

2.4 ( ) ( B ) A B F (1) W = B A F dr. A F q dr f(x,y,z) A B Γ( ) Minoru TANAKA (Osaka Univ.) I(2011), Sec p. 1/30

, 1.,,,.,., (Lin, 1955).,.,.,.,. f, 2,. main.tex 2011/08/13( )

TOP URL 1


II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2

66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3) d 1 NN K K 8.1 d σd σd M = σd = E 2 d (8.4) ρ 2 d = I M = EI ρ 1 ρ = M EI ρ EI

Fr

Transcription:

KENZOU 2008 8 2 3 2 3 2 2 4 2 4............................................... 2 4.2............................... 3 4.2........................................... 4 4.3.............................. 5 4.3............................. 5 4.3.2.......................... 7 4.3.3......................................... 7 4.4......................................... 8 4.5............................................... 9 4.5................................................ 9 4.5.2........................................... 0 4.5.3...................................... A 2........................................... 2......................................... 3...................................... 3 ============================

4 v = v t + (v v = K p (4. A ( B = ( BA (A B (v v = ( v v v rot v ( v x ( v v = v x x, v v y y y, v v z z = z 2... (v v = 2 q2 v rot v ( vx 2 x, v2 y y, v2 z = z 2 q2 (q = v v t = K p 2 q2 + v ω, ( ω = rot v (4.2 p P dp = dp P = p dp (4.3 P = p (4.4 4.2 v (P t = K + 2 q2 + v ω (4.5 4. φ v v = φ 2 3.8. ( φ K = t + 2 q2 + P (4.6 K K U K = U 4.2 ( φ t + 2 q2 + P + U = 0 (4.7 ( φ φ 4.7 x, φ y, φ = 0 z φ t 4.7 t f(t φ t + 2 q2 + P + U = f(t (4.8 4.8 2

4.2 v/ t=0 K = U 4.5 ( 2 q2 + P + U = v ω (4.9 H = 2 q2 + P + U (4.0 ω = 0ω / v v ω = 0 H = const 4.0 2 3 H = const P = p/ U = gz p + 2 q2 + gz = const (4. const const -7 20m/sec m F ig.5 v P z v 2 P 2 z 2 P + 2 v2 + gz = P 2 + 2 v 2 2 + gz 2... z 2 z = 2g (v2 v2 2 + P P 2 g P = P 2 v 2 = 0 v = 20 z 2 z = 20.4m -8 Q q θ Fig.6 Q 2 Q 3 F ig.6 Q 2 q 2 Q θ P P 2 θ q F P 3 y x q 3 Q 3 3

x, y Fig.6 Q = Q 2 + Q 3 (4.2 p + 2 q 2 = p + 2 q 2 2 = p + 2 q 3 2... q = q 2 = q 3 (4.3 x Q q cos θ Q 2 q 2, Q 3 q 3 Q q cos θ = Q 2 q 2 Q 3 q 3 (4.4 4.34.4 Q 2 Q 3 = Q cos θ (4.5 4.24.5 Q 2 Q 3 Q 2 = ( + cos θq /2, Q 3 = ( cos θq /2 F F = P (P 2 cos θ P sin θ P = Q q, P 2 = ( + cos θq q 2 /2, P 3 = ( cos θq q 3 /2 F = Q q {( + cos θq 2 /2 ( cos θq 3 /2} Q cos θ = Q q sin 2 θ 4.2. 3.4. 3.40 P p = k γ k (4.6 kγ γ P = dp = γ p γ (4.7 p = 0 P = 0 U = 0 2 q2 + γ γ c 2 q2 + P = const (4.8 p = γ 2 c = const, (4.9 c 2 = γ P (4.20 q = 0 0 4.9 2 q2 + γ c2 = γ c2 0 (4.2 4

c 2 c 2 0 = q2 2 qm 2, q m = γ c 0 (4.22 q q m q m 4.64.20 p c 2/(γ, p γ c 2γ/(γ 4.22 = ( q2 γ 0 qm 2 p = ( γ q2 γ p 0 qm 2 (4.23 ( γ } p q = q m { 2 γ p 0 (4.24 p 0 p q 4.3 4.8 Fig.7 v q s φ φ = q(s, φ = q(s (4.25 s 4.3. q = Q Q t t 4.25 φ = q(ts φ t + 2 q2 + p ( + gz = f(t s + dt 2 q2 + p + gz = f(t (4.26 y F ig.7 2 F ig.8 p 2 q p 0 p z 2 z s x h l 2 p q 5

Fig.7 p z qs + 2 q2 + p + gz = qs + 2 q2 + p + gz (4.27 p p = g(z z q(s s (4.28 4.28 q q 2 p 2 4.27 q = s 2 s { } (p 2 p + g(z 2 z (4.29-9 Fig.8 l 2 z = z 2 = 0 p 2 = p s 2 s = l 4.29 q = l (p p (4.30 p p 4.304.3 p + gh = p + 2 q2 (4.3 q = 2l ( q2 q 2, ( q = 2gh (4.32 q 0 dq q 2 q 2 = t... q = q tanh t 2T, 0 2l dt ( q tanh = t q q 2l ( T = l/q q q p 4.3 ( p = p + gh tanh 2 t = p + gh sech 2 t 2T 2T t = 0 p + gh p Fig.9 q = 0p = 0l =, h = (4.33 F ig.9 qp q q = 0 tanh 5t p = 9.8sech 2 5t t 6

4.3.2 s q(s, t(s = Q(t q s t q = Q(t (s 4.25 φ = q = Q(t (s (4.34 (4.35 4.26 φ + 2 Q2 2 + p + gz = f(t (4.36 p p = g(z z Q s2 ( 2 Q2 2 2 Q s (4.37 s2 Q s + ( 2 Q2 2 2 2 + p 2 p + g(z 2 z = 0 (4.38-20 9 0 l p 2 = p = p, z 2 z = h 2 = 0 4.38 Q s2 s + 2 Q2 0 2 gh = 0 (4.39 s s2 s Q Q = 0 q l 0 0 = l 0 l q + 2 q2 gh = 0 q = 2l (q2 q 2 (q = 2gh (4.40-9 4.32-9 s = R / 4.3.3 K 2 3.33 v = (v v = p (4.4 F ig.20 R n R n s t 7

Fig.20 st q v = qt f s = t f = t t s s ( v v = q s q t (qt = q t + q2 s s nr κ t s = R n, 4.4 κ = R (4.42 p = q 2 2 s t q2 κn (4.43 p s t n p s = q 2 2 s, p n = κq2 (4.44 4.44 2 2 4.44 4.3 P p s = s ( p dp p ( p dp s + 2 q2 = 0 P + 2 q2 = const (4.45 s 4.4 2 3.8 ω 2 Ω K = U p 4.5 v (P t = + U + 2 q2 + v ω rot rot(dv/dt = ω/ trot = 0 ω t = rot(v ω (4.46 rotv ω = v( ω ω( v + (ω v (v ω 2 (3.6 = t + v 2 (3.3 v = 8

4.46 rot(v ω = ω t... = v( ω ω( v + (ω v (v ω = ω + (ω v (v ω = ω (v ω... ω = ω ( ω = ω + (v ω t + (ω v (4.47 4.47 ( ω = ω ω 2 ( ( ω ω = v (4.48 4.474.48 t = 0 ω = 0 4.48 [ ( ] {( } ω ω = v = 0 (4.49 t=0 t=0 t ( ω = t= t ( [ ω + t=0 ( ] ω t = 0 (4.50 t=0 ω = 0 t = 0 ω 0 ω = 0 t = 0 ω = 0 4.5 4.5. Γ( = v dr = v s = (udx + vdy + wdz = ( φ φ φ dx + dy + x y z dz = dφ (4.5 circulationγ( v s v φ 2 rotv = ω Γ( = v dr = (rotv n d (4.52 Γ( = ω n d = ωd (4.53 Γ( = 0 2 2! div! =! = rotv = 0 9

Fig.2- Γ Γ ( AB A B ( B A Γ ( F ig.2 F ig.2 2 A B A Γ Γ Γ A Γ Γ ( = 0 Γ ( = + AB + + = Γ + + = Γ ( Γ( = 0 BA AB AB... Γ ( = Γ( (4.54 3 A ΓA Γ Fig.2-2 AA A AA ω n d ω n = 0 + = Γ( + Γ( = 0 AA + A A + A A AA... Γ( = Γ( (4.55 4.5.2 ω n σ Γ( = ω n d = ω d = ωσ (4.56 Γ( ω Γ( = ω n d = ωσ (4.57 3 0

Γ( 4.5.3 t = 0 0 t Γ( F ig.22 t = 0 0 t = t 4 Γ( = v dr = (v dr c v (v dr = dr + v dr (4.58 K 4.4.4 v dp = (U + P, K = U, P = 2 r r 2 dr = r 2 r 4.58... (4.59 dr = (r 2 r = v 2 v = dv (4.60 ( (v dr = (U + P dr + v dv = d(u + P + d ] Γ( = [ 2 q2 U P 2 v2 ( = d 2 q2 U P (4.6 q P U Γ( = const = Γ( 0 (4.62 4 2 3.

( 3 3 2 3 A r r = r(t = (x(t, y(t, z(t (A. t a t b s s [t 0, t] P Q[ t, t + t ] P Q ( x P Q = 2 ( 2 ( 2 y z ( x 2 + ( y 2 + ( z 2 = + + t t t t (dx.. 2 ( 2 ( 2 dy dz. = lim P Q = + + dt (A.2 t 0 dt dt dt.. s t (dx 2 ( 2 ( 2 dy dz t. s = = + + dt = dr s 0 dt dt dt dt dt (A.3 t 0 t s s t 0 r = r(s (A.4 2

F ig.a dr dt F ig.a 2 φ dφ = u φ u = P r(s r Q r(s + s P θ u dφ O s s r rs + s Q r = P Q r s s 0 t s t = dr t Q P θ κ = dθ = lim θ s 0 s κ = /κ (A.5 (A.6 φ(x, y, z P u P u P s r(s P φ u φ(r(s u φ(p + su φ(p = lim = dφ s 0 s = φ x x s + φ y y s + φ z z s = u φ φ(x, y, z n φ dφ/dn (A.7 φ = dφ n (A.8 v dr = (rotv nd (A.9 F ig.a 3 n v dr 3

2024 © docsplayer.net プライバシー | 利用規約 | フィードバック