: ( ) : ( ) :! ( ) / 32
|
|
- れんま たけはな
- 5 years ago
- Views:
Transcription
1 ( ) / 32
2 : ( ) : ( ) :! ( ) / 32
3 ( ) / 32
4 ( ) ( ) ( : ) 1 2 (2014) 1 M2 2 ( ) / 32
5 ( ) ( ) ( : ) 1 2 (2014) YouTube, Chladni, 1 M2 2 ( ) / 32
6 ( ) ( ) ( : ) 1 2 (2014) YouTube, Chladni, 9/27( ) 1 M2 2 ( ) / 32
7 : (, ) ( ) ( ) / 32
8 (,, ) ( ) Entdeckungen über die Theorie des Klanges (, 1787) Die Akustik (, 1802) Neue Beyträge zur Akustik (, 1817) ( ) m n ( ) / 32
9 ( ) / 32
10 ( ) / 32
11 ( ) / 32
12 ( ) ( ) / 32
13 ( ) : ( ) ( ) / 32
14 1808 ( ) (1811, 1813, 1815) - (1850) - 2 ( u 4 ) t 2 = D u x u x 2 y u y 4 u = u(x, y, t) (x, y) t ( ) / 32
15 ( ) / 32
16 ( ) / 32
17 ( ) ( ) / 32
18 ( ) 1 ( ) 2 ( ) / 32
19 ( ) 1 ( ) 2 ( ) ( ) / 32
20 ( ) 1 ( ) 2 ( ) 20 ( 100 ) ( ) (1909 ) ( ) ( ) / 32
21 : 1 ( ) 2 ( ) 3 ( ) ( ) / 32
22 : 1 ( ) 2 ( ) 3 ( ) ( ) / 32
23 ( : ) ( ) (normal mode of vibration) ( ) / 32
24 : ( ) (, ) ( ) / 32
25 : ( ) (, ) ( ) T T = 2π l g (g = 9.8 [ms 2 ] ( ), l ) ( ) ( ) / 32
26 : ( ) ( ) / 32
27 : ( ) θ = A sin (ωt + ϕ), ω = 2π T ( ). A, ϕ T ( ω ) ( ) / 32
28 ( ) / 32
29 A 1 (x) = a 1 sin πx L, A 2(x) = a 2 sin 2πx L, A 3(x) = a 3 sin 3πx L, ( ) ( ) n A n (x) = a n sin nπx L. ( ) / 32
30 ( )? u n = A n (x)sin(ω n t + ϕ n ) = a n sin nπx L (ω n = nπc L ) ( nπc ) sin L t + ϕ n. (x A n (x) ) ( ) / 32
31 ( ) u = A 1 (x) sin (ω 1 t + ϕ 1 ) + A 2 (x) sin (ω 2 t + ϕ 2 ) + = n=1 A n (x) sin (ω n t + ϕ n ), A n (x) = a n sin nπx L. ( ) / 32
32 ( ) u = A 1 (x) sin (ω 1 t + ϕ 1 ) + A 2 (x) sin (ω 2 t + ϕ 2 ) + = A n (x) sin (ω n t + ϕ n ), n=1 A n (x) = a n sin nπx L. = A n (x) = a n sin nπx L ω n ( ) / 32
33 , ( ) / 32
34 : (the Tacoma Narrows Bridge) m ( ) / 32
35 ( [1]) ( ) / 32
36 ( ) ( ) / 32
37 ( ) / 32
38 ( [1]) ( WWW ) ( ) / 32
39 ( ) m = n m, n 1 m = n D 4 2 m = n D 4 3 m > n D 4 4 m > n D 4 5 m > n D 4 6 m > n D 4 7 m > n D 2 D n ( n, ). D 4 90 D ( ) / 32
40 ( ) m = n m, n 1 m = n D 4 2 m = n D 4 3 m > n D 4 4 m > n D 4 5 m > n D 4 6 m > n D 4 7 m > n D 2 D n ( n, ). D 4 90 D ( ) / 32
41 (Mary Désirée Waller, , ) Chladni Figures study in symmetry (1961) ( ) ( ) / 32
42 ( ) ( M2) ( [5], 2015/9/9) ( ) / 32
43 (oscillation, vibration) ( ) ( ;,, ) ( ) ( X ) ( ) / 32
44 ( ) 100 ( ) / 32
45 ( ) 100 ( ) / 32
46 Mary D. Waller, Vibrations of free square plates: part I. normal vibrating modes, Physical Society, Vol. 51 (1939), pp Mary D. Waller, Chladni figures a study in symmetry, G. Bell (1961). von Walter Ritz, Theorie der Transversalschwingungen einer quadratischen Platte mit freien Rändern, Annalen der Physik Volume 333, Issue 4, pp (1909).,,, ,,, Chladni, 2015, ,. ( ) / 32
47 : 1 ( ) 200 (2006) ( ) ( ) ( ) / 32
48 ( ) / 32
49 : ( 0) x kx (k, ) 2 mα(t) = kx(t). x (t) = α(t) = k m x(t) = ω2 x(t) (ω = x (t) = ω 2 x(t) k m ). ( ) / 32
50 : x(t) = C 1 sin ωt + C 2 cos ωt ( ) x(t) = A sin(ωt + ϕ) x (t) = ω 2 x(t) T = 2π ω = 2π m k. ( ) ( ) / 32
51 : x(t) = C 1 sin ωt + C 2 cos ωt ( ) x(t) = A sin(ωt + ϕ) x (t) = ω 2 x(t) T = 2π ω = 2π m k. ( ) ( ) ( ) / 32
85 4
85 4 86 Copright c 005 Kumanekosha 4.1 ( ) ( t ) t, t 4.1.1 t Step! (Step 1) (, 0) (Step ) ±V t (, t) I Check! P P V t π 54 t = 0 + V (, t) π θ : = θ : π ) θ = π ± sin ± cos t = 0 (, 0) = sin π V + t +V
More information29 21 3 1 1 2 1.1............................ 2 1.2................................... 2 2 3 2.1 Neumann...................... 3 2.2............................. 5 2.3.................................
More informationBanach-Tarski Hausdorff May 17, 2014 3 Contents 1 Hausdorff 5 1.1 ( Unlösbarkeit des Inhaltproblems) 5 5 1 Hausdorff Banach-Tarski Hausdorff [H1, H2] Hausdorff Grundzüge der Mangenlehre [H1] Inhalte
More information重力方向に基づくコントローラの向き決定方法
( ) 2/Sep 09 1 ( ) ( ) 3 2 X w, Y w, Z w +X w = +Y w = +Z w = 1 X c, Y c, Z c X c, Y c, Z c X w, Y w, Z w Y c Z c X c 1: X c, Y c, Z c Kentaro Yamaguchi@bandainamcogames.co.jp 1 M M v 0, v 1, v 2 v 0 v
More informationGmech08.dvi
145 13 13.1 13.1.1 0 m mg S 13.1 F 13.1 F /m S F F 13.1 F mg S F F mg 13.1: m d2 r 2 = F + F = 0 (13.1) 146 13 F = F (13.2) S S S S S P r S P r r = r 0 + r (13.3) r 0 S S m d2 r 2 = F (13.4) (13.3) d 2
More information…_…C…L…fi…J…o†[fiü“ePDF/−mflF™ƒ
80 80 80 3 3 5 8 10 12 14 14 17 22 24 27 33 35 35 37 38 41 43 46 47 50 50 52 54 56 56 59 62 65 67 71 74 74 76 80 83 83 84 87 91 91 92 95 96 98 98 101 104 107 107 109 110 111 111 113 115
More informationGmech08.dvi
63 6 6.1 6.1.1 v = v 0 =v 0x,v 0y, 0) t =0 x 0,y 0, 0) t x x 0 + v 0x t v x v 0x = y = y 0 + v 0y t, v = v y = v 0y 6.1) z 0 0 v z yv z zv y zv x xv z xv y yv x = 0 0 x 0 v 0y y 0 v 0x 6.) 6.) 6.1) 6.)
More information#A A A F, F d F P + F P = d P F, F y P F F x A.1 ( α, 0), (α, 0) α > 0) (x, y) (x + α) 2 + y 2, (x α) 2 + y 2 d (x + α)2 + y 2 + (x α) 2 + y 2 =
#A A A. F, F d F P + F P = d P F, F P F F A. α, 0, α, 0 α > 0, + α +, α + d + α + + α + = d d F, F 0 < α < d + α + = d α + + α + = d d α + + α + d α + = d 4 4d α + = d 4 8d + 6 http://mth.cs.kitmi-it.c.jp/
More informationGmech08.dvi
51 5 5.1 5.1.1 P r P z θ P P P z e r e, z ) r, θ, ) 5.1 z r e θ,, z r, θ, = r sin θ cos = r sin θ sin 5.1) e θ e z = r cos θ r, θ, 5.1: 0 r
More information1. 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
IB IIA 1 1 r, θ, φ 1 (r, θ, φ)., r, θ, φ 0 r
More information知能科学:ニューラルネットワーク
2 3 4 (Neural Network) (Deep Learning) (Deep Learning) ( x x = ax + b x x x ? x x x w σ b = σ(wx + b) x w b w b .2.8.6 σ(x) = + e x.4.2 -.2 - -5 5 x w x2 w2 σ x3 w3 b = σ(w x + w 2 x 2 + w 3 x 3 + b) x,
More information知能科学:ニューラルネットワーク
2 3 4 (Neural Network) (Deep Learning) (Deep Learning) ( x x = ax + b x x x ? x x x w σ b = σ(wx + b) x w b w b .2.8.6 σ(x) = + e x.4.2 -.2 - -5 5 x w x2 w2 σ x3 w3 b = σ(w x + w 2 x 2 + w 3 x 3 + b) x,
More information1 3 1.1.......................... 3 1............................... 3 1.3....................... 5 1.4.......................... 6 1.5........................ 7 8.1......................... 8..............................
More informationKorteweg-de Vries
Korteweg-de Vries 2011 03 29 ,.,.,.,, Korteweg-de Vries,. 1 1 3 1.1 K-dV........................ 3 1.2.............................. 4 2 K-dV 5 2.1............................. 5 2.2..............................
More informationx A Aω ẋ ẋ 2 + ω 2 x 2 = ω 2 A 2. (ẋ, ωx) ζ ẋ + iωx ζ ζ dζ = ẍ + iωẋ = ẍ + iω(ζ iωx) dt dζ dt iωζ = ẍ + ω2 x (2.1) ζ ζ = Aωe iωt = Aω cos ωt + iaω sin
2 2.1 F (t) 2.1.1 mẍ + kx = F (t). m ẍ + ω 2 x = F (t)/m ω = k/m. 1 : (ẋ, x) x = A sin ωt, ẋ = Aω cos ωt 1 2-1 x A Aω ẋ ẋ 2 + ω 2 x 2 = ω 2 A 2. (ẋ, ωx) ζ ẋ + iωx ζ ζ dζ = ẍ + iωẋ = ẍ + iω(ζ iωx) dt dζ
More informationm 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
m v = mg + kv m v = mg k v v m v = mg + kv α = mg k v = α e rt + e rt m v = mg + kv v mg + kv = m v α + v = k m v (v α (v + α = k m ˆ ( v α ˆ αk v = m v + α ln v α v + α = αk m t + C v α v + α = e αk m
More informationlim lim lim lim 0 0 d lim 5. d 0 d d d d d d 0 0 lim lim 0 d
lim 5. 0 A B 5-5- A B lim 0 A B A 5. 5- 0 5-5- 0 0 lim lim 0 0 0 lim lim 0 0 d lim 5. d 0 d d d d d d 0 0 lim lim 0 d 0 0 5- 5-3 0 5-3 5-3b 5-3c lim lim d 0 0 5-3b 5-3c lim lim lim d 0 0 0 3 3 3 3 3 3
More informationω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 +
2.6 2.6.1 ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j (2.121) Z ω ω j γ j f j
More informationẍ = kx, (k > ) (.) x x(t) = A cos(ωt + α) (.). d/ = D. d dt x + k ( x = D + k ) ( ) ( ) k k x = D + i D i x =... ( ) k D + i x = or ( ) k D i x =.. k.
K E N Z OU 8 9 8. F = kx x 3 678 ẍ = kx, (k > ) (.) x x(t) = A cos(ωt + α) (.). d/ = D. d dt x + k ( x = D + k ) ( ) ( ) k k x = D + i D i x =... ( ) k D + i x = or ( ) k D i x =.. k. D = ±i dt = ±iωx,
More informationII Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R
II Karel Švadlenka 2018 5 26 * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* 5 23 1 u = au + bv v = cu + dv v u a, b, c, d R 1.3 14 14 60% 1.4 5 23 a, b R a 2 4b < 0 λ 2 + aλ + b = 0 λ =
More information数学演習:微分方程式
( ) 1 / 21 1 2 3 4 ( ) 2 / 21 x(t)? ẋ + 5x = 0 ( ) 3 / 21 x(t)? ẋ + 5x = 0 x(t) = t 2? ẋ = 2t, ẋ + 5x = 2t + 5t 2 0 ( ) 3 / 21 x(t)? ẋ + 5x = 0 x(t) = t 2? ẋ = 2t, ẋ + 5x = 2t + 5t 2 0 x(t) = sin 5t? ẋ
More informationm 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
3 3.1 ( 1 m d2 x(t dt 2 = kx(t k = (3.1 d 2 x dt 2 = ω2 x, ω = x(t = 0, ẋ(0 = v 0 k m (3.2 x = v 0 ω sin ωt (ẋ = v 0 cos ωt (3.3 E = 1 2 mẋ2 + 1 2 kx2 = 1 2 mv2 0 cos 2 ωt + 1 2 k v2 0 ω 2 sin2 ωt = 1
More information2005 2006.2.22-1 - 1 Fig. 1 2005 2006.2.22-2 - Element-Free Galerkin Method (EFGM) Meshless Local Petrov-Galerkin Method (MLPGM) 2005 2006.2.22-3 - 2 MLS u h (x) 1 p T (x) = [1, x, y]. (1) φ(x) 0.5 φ(x)
More information64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () m/s : : a) b) kg/m kg/m k
63 3 Section 3.1 g 3.1 3.1: : 64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () 3 9.8 m/s 2 3.2 3.2: : a) b) 5 15 4 1 1. 1 3 14. 1 3 kg/m 3 2 3.3 1 3 5.8 1 3 kg/m 3 3 2.65 1 3 kg/m 3 4 6 m 3.1. 65 5
More informationp = mv p x > h/4π λ = h p m v Ψ 2 Ψ
II p = mv p x > h/4π λ = h p m v Ψ 2 Ψ Ψ Ψ 2 0 x P'(x) m d 2 x = mω 2 x = kx = F(x) dt 2 x = cos(ωt + φ) mω 2 = k ω = m k v = dx = -ωsin(ωt + φ) dt = d 2 x dt 2 0 y v θ P(x,y) θ = ωt + φ ν = ω [Hz] 2π
More information1. 4cm 16 cm 4cm 20cm 18 cm L λ(x)=ax [kg/m] A x 4cm A 4cm 12 cm h h Y 0 a G 0.38h a b x r(x) x y = 1 h 0.38h G b h X x r(x) 1 S(x) = πr(x) 2 a,b, h,π
. 4cm 6 cm 4cm cm 8 cm λ()=a [kg/m] A 4cm A 4cm cm h h Y a G.38h a b () y = h.38h G b h X () S() = π() a,b, h,π V = ρ M = ρv G = M h S() 3 d a,b, h 4 G = 5 h a b a b = 6 ω() s v m θ() m v () θ() ω() dθ()
More informationchap1.dvi
1 1 007 1 e iθ = cos θ + isin θ 1) θ = π e iπ + 1 = 0 1 ) 3 11 f 0 r 1 1 ) k f k = 1 + r) k f 0 f k k = 01) f k+1 = 1 + r)f k ) f k+1 f k = rf k 3) 1 ) ) ) 1+r/)f 0 1 1 + r/) f 0 = 1 + r + r /4)f 0 1 f
More informationm(ẍ + γẋ + ω 0 x) = ee (2.118) e iωt P(ω) = χ(ω)e = ex = e2 E(ω) m ω0 2 ω2 iωγ (2.119) Z N ϵ(ω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j (2.120)
2.6 2.6.1 mẍ + γẋ + ω 0 x) = ee 2.118) e iωt Pω) = χω)e = ex = e2 Eω) m ω0 2 ω2 iωγ 2.119) Z N ϵω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j 2.120) Z ω ω j γ j f j f j f j sum j f j = Z 2.120 ω ω j, γ ϵω) ϵ
More informationuntitled
1 2 3 4 5 6 40 97,391 144 0.001479 0.998521 41 97,247 157 0.001614 0.998386 42 97,090 171 0.001761 0.998239 43 96,919 186 0.001919 0.998081 44 96,733 204 0.002109 0.997891 45 96,529 223 0.002310 0.997690
More informationLLG-R8.Nisus.pdf
d M d t = γ M H + α M d M d t M γ [ 1/ ( Oe sec) ] α γ γ = gµ B h g g µ B h / π γ g = γ = 1.76 10 [ 7 1/ ( Oe sec) ] α α = λ γ λ λ λ α γ α α H α = γ H ω ω H α α H K K H K / M 1 1 > 0 α 1 M > 0 γ α γ =
More informationv_-3_+2_1.eps
I 9-9 (3) 9 9, x, x (t)+a(t)x (t)+b(t)x(t) = f(t) (9), a(t), b(t), f(t),,, f(t),, a(t), b(t),,, x (t)+ax (t)+bx(t) = (9),, x (t)+ax (t)+bx(t) = f(t) (93), b(t),, b(t) 9 x (t), x (t), x (t)+a(t)x (t)+b(t)x(t)
More information<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63>
高速流体力学 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. http://www.morikita.co.jp/books/mid/067361 このサンプルページの内容は, 第 1 版発行時のものです. i 20 1999 3 2 2010 5 ii 1 1 1.1 1 1.2 4 9 2 10 2.1 10 2.2 12 2.3 13 2.4 13 2.5
More information2. 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
1. 1 213 1 6 1 3 1: ( ) 2: 3: SF 1 2 3 1: 3 2 A m 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
More informationA (1) = 4 A( 1, 4) 1 A 4 () = tan A(0, 0) π A π
4 4.1 4.1.1 A = f() = f() = a f (a) = f() (a, f(a)) = f() (a, f(a)) f(a) = f 0 (a)( a) 4.1 (4, ) = f() = f () = 1 = f (4) = 1 4 4 (4, ) = 1 ( 4) 4 = 1 4 + 1 17 18 4 4.1 A (1) = 4 A( 1, 4) 1 A 4 () = tan
More information6 2 2 x y x y t P P = P t P = I P P P ( ) ( ) ,, ( ) ( ) cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ y x θ x θ P
6 x x 6.1 t P P = P t P = I P P P 1 0 1 0,, 0 1 0 1 cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ x θ x θ P x P x, P ) = t P x)p ) = t x t P P ) = t x = x, ) 6.1) x = Figure 6.1 Px = x, P=, θ = θ P
More informationA = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B
9 7 A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B x x B } B C y C y + x B y C x C C x C y B = A
More information(1) 3 A B E e AE = e AB OE = OA + e AB = (1 35 e ) e OE z 1 1 e E xy e = 0 e = 5 OE = ( 2 0 0) E ( 2 0 0) (2) 3 E P Q k EQ = k EP E y 0
(1) 3 A B E e AE = e AB OE = OA + e AB = (1 35 e 0 1 15 ) e OE z 1 1 e E xy 5 1 1 5 e = 0 e = 5 OE = ( 2 0 0) E ( 2 0 0) (2) 3 E P Q k EQ = k EP E y 0 Q y P y k 2 M N M( 1 0 0) N(1 0 0) 4 P Q M N C EP
More information( ) e + e ( ) ( ) e + e () ( ) e e Τ ( ) e e ( ) ( ) () () ( ) ( ) ( ) ( )
n n (n) (n) (n) (n) n n ( n) n n n n n en1, en ( n) nen1 + nen nen1, nen ( ) e + e ( ) ( ) e + e () ( ) e e Τ ( ) e e ( ) ( ) () () ( ) ( ) ( ) ( ) ( n) Τ n n n ( n) n + n ( n) (n) n + n n n n n n n n
More information08-Note2-web
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)
More information() 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)
0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()
More information孫文について
1924 1 1 165 ( ) 3 1987 YouTube http://www.youtube.com/watch?v=mttee1lhbkg http://www.youtube.com/watch?v=ibyhsmir9fa&list=pl8fdacdbcb7a4b2a7 http://www.youtube.com/watch?v=cppajh6il5q&list=pl96acdb31e24545b7
More information2 (2016 3Q N) c = o (11) Ax = b A x = c A n I n n n 2n (A I n ) (I n X) A A X A n A A A (1) (2) c 0 c (3) c A A i j n 1 ( 1) i+j A (i, j) A (i, j) ã i
[ ] (2016 3Q N) a 11 a 1n m n A A = a m1 a mn A a 1 A A = a n (1) A (a i a j, i j ) (2) A (a i ca i, c 0, i ) (3) A (a i a i + ca j, j i, i ) A 1 A 11 0 A 12 0 0 A 1k 0 1 A 22 0 0 A 2k 0 1 0 A 3k 1 A rk
More information34号 目 次
1932 35 1939 π 36 37 1937 12 28 1998 2002 1937 20 ª 1937 2004 1937 12 º 1937 38 11 Ω 1937 1943 1941 39 æ 1936 1936 1936 10 1938 25 35 40 2004 4800 40 ø 41 1936 17 1935 1936 1938 1937 15 2003 28 42 1857
More informationma22-9 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
A 2. x F (t) =f sin ωt x(0) = ẋ(0) = 0 ω θ sin θ θ 3! θ3 v = f mω cos ωt x = f mω (t sin ωt) ω t 0 = f ( cos ωt) mω x ma2-2 t ω x f (t mω ω (ωt ) 6 (ωt)3 = f 6m ωt3 2.2 u ( v w) = v ( w u) = w ( u v) ma22-9
More information, 3, 6 = 3, 3,,,, 3,, 9, 3, 9, 3, 3, 4, 43, 4, 3, 9, 6, 6,, 0 p, p, p 3,..., p n N = p p p 3 p n + N p n N p p p, p 3,..., p n p, p,..., p n N, 3,,,,
6,,3,4,, 3 4 8 6 6................................. 6.................................. , 3, 6 = 3, 3,,,, 3,, 9, 3, 9, 3, 3, 4, 43, 4, 3, 9, 6, 6,, 0 p, p, p 3,..., p n N = p p p 3 p n + N p n N p p p,
More information1 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
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 0 < t < τ I II 0 No.2 2 C x y x y > 0 x 0 x > b a dx
More information2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h)
1 16 10 5 1 2 2.1 a a a 1 1 1 2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h) 4 2 3 4 2 5 2.4 x y (x,y) l a x = l cot h cos a, (3) y = l cot h sin a (4) h a
More informationr d 2r d l d (a) (b) (c) 1: I(x,t) I(x+ x,t) I(0,t) I(l,t) V in V(x,t) V(x+ x,t) V(0,t) l V(l,t) 2: 0 x x+ x 3: V in 3 V in x V (x, t) I(x, t
1 1 2 2 2r d 2r d l d (a) (b) (c) 1: I(x,t) I(x+ x,t) I(0,t) I(l,t) V in V(x,t) V(x+ x,t) V(0,t) l V(l,t) 2: 0 x x+ x 3: V in 3 V in x V (x, t) I(x, t) V (x, t) I(x, t) V in x t 3 4 1 L R 2 C G L 0 R 0
More informationohp_06nov_tohoku.dvi
2006 11 28 1. (1) ẋ = ax = x(t) =Ce at C C>0 a0 x(t) 0(t )!! 1 0.8 0.6 0.4 0.2 2 4 6 8 10-0.2 (1) a =2 C =1 1. (1) τ>0 (2) ẋ(t) = ax(t τ) 4 2 2 4 6 8 10-2 -4 (2) a =2 τ =1!! 1. (2) A. (2)
More informationQMI_09.dvi
25 3 19 Erwin Schrödinger 1925 3.1 3.1.1 3.1.2 σ τ 2 2 ux, t) = ux, t) 3.1) 2 x2 ux, t) σ τ 2 u/ 2 m p E E = p2 3.2) E ν ω E = hν = hω. 3.3) k p k = p h. 3.4) 26 3 hω = E = p2 = h2 k 2 ψkx ωt) ψ 3.5) h
More informationQMI_10.dvi
25 3 19 Erwin Schrödinger 1925 3.1 3.1.1 σ τ x u u x t ux, t) u 3.1 t x P ux, t) Q θ P Q Δx x + Δx Q P ux + Δx, t) Q θ P u+δu x u x σ τ P x) Q x+δx) P Q x 3.1: θ P θ Q P Q equation of motion P τ Q τ σδx
More informationS04S006 S04S023
S04S006 S04S023 0 2 1 3 2 7 3 16 4 19 5 Poincaré-Hopf 22 6 25 A 1 27 1 0 Poincaré-Hopf X V X = c 1 c n p p V i(v ; p) V i(v ) c i V c i s(v ; c i ) n i(v ) = χ(x) (s(v ; c i ) 1) i=1 χ(x) X 1 2 3 3 Poincaré-Hopf
More information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)
More information1.2 y + P (x)y + Q(x)y = 0 (1) y 1 (x), y 2 (x) y 1 (x), y 2 (x) (1) y(x) c 1, c 2 y(x) = c 1 y 1 (x) + c 2 y 2 (x) 3 y 1 (x) y 1 (x) e R P (x)dx y 2
1 1.1 R(x) = 0 y + P (x)y + Q(x)y = R(x)...(1) y + P (x)y + Q(x)y = 0...(2) 1 2 u(x) v(x) c 1 u(x)+ c 2 v(x) = 0 c 1 = c 2 = 0 c 1 = c 2 = 0 2 0 2 u(x) v(x) u(x) u (x) W (u, v)(x) = v(x) v (x) 0 1 1.2
More information(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x
Compton Scattering Beaming exp [i k x ωt] k λ k π/λ ω πν k ω/c k x ωt ω k α c, k k x ωt η αβ k α x β diag + ++ x β ct, x O O x O O v k α k α β, γ k γ k βk, k γ k + βk k γ k k, k γ k + βk 3 k k 4 k 3 k
More information43-03‘o’ì’¹‘®”q37†`51†i„¤‰ƒ…m†[…g†j.pwd
n 808 3.0 % 86.8 % 8.3 % n 24 4.1 % 54.0 % 37.5 % 0% % 20 % 30 % 40 % 50 % 60 % 70 % 80 % 90 % 0% 37.4 % 7.2 % 27.2 % 8.4 % n 648 13.6 % 18.1% 45.4 % 4.1% n 18 0% % 20 % 30 % 40 % 50 % 60 % 70 % 80 % 90
More informationx,, 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
12 -- 1 4 2009 9 4-1 4-2 4-3 4-4 4-5 4-6 4-7 4-8 4-9 4-10 c 2011 1/(13) 4--1 2009 9 3 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
More information1 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
. ( + + 5 d ( + + 5 ( + + + 5 + + + 5 + + 5 y + + 5 dy ( + + dy + + 5 y log y + C log( + + 5 + C. ++5 (+ +4 y (+/ + + 5 (y + 4 4(y + dy + + 5 dy Arctany+C Arctan + y ( + +C. + + 5 ( + log( + + 5 Arctan
More informationhttp://www.ns.kogakuin.ac.jp/~ft13389/lecture/physics1a2b/ pdf I 1 1 1.1 ( ) 1. 30 m µm 2. 20 cm km 3. 10 m 2 cm 2 4. 5 cm 3 km 3 5. 1 6. 1 7. 1 1.2 ( ) 1. 1 m + 10 cm 2. 1 hr + 6400 sec 3. 3.0 10 5 kg
More informationTOP URL 1
TOP URL http://amonphys.web.fc2.com/ 1 30 3 30.1.............. 3 30.2........................... 4 30.3...................... 5 30.4........................ 6 30.5.................................. 8 30.6...............................
More information1 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
sin cos P (primary) S (secondly) 2 P S A sin(ω2πt + α) A ω ω α 3 3 2 2V 3 33+.6T m T 5 34m Hz. 34 3.4m 2 36km 5Hz. 36km m 34 m 5 34 + m 5 33 5 =.66m 34m 34 x =.66 55Hz, 35 5 =.7 485.7Hz 2 V 5Hz.5V.5V V
More informationさくらの個別指導 ( さくら教育研究所 ) A a 1 a 2 a 3 a n {a n } a 1 a n n n 1 n n 0 a n = 1 n 1 n n O n {a n } n a n α {a n } α {a
... A a a a 3 a n {a n } a a n n 3 n n n 0 a n = n n n O 3 4 5 6 n {a n } n a n α {a n } α {a n } α α {a n } a n n a n α a n = α n n 0 n = 0 3 4. ()..0.00 + (0.) n () 0. 0.0 0.00 ( 0.) n 0 0 c c c c c
More information1 (1) ( i ) 60 (ii) 75 (iii) 315 (2) π ( i ) (ii) π (iii) 7 12 π ( (3) r, AOB = θ 0 < θ < π ) OAB A 2 OB P ( AB ) < ( AP ) (4) 0 < θ < π 2 sin θ
1 (1) ( i ) 60 (ii) 75 (iii) 15 () ( i ) (ii) 4 (iii) 7 1 ( () r, AOB = θ 0 < θ < ) OAB A OB P ( AB ) < ( AP ) (4) 0 < θ < sin θ < θ < tan θ 0 x, 0 y (1) sin x = sin y (x, y) () cos x cos y (x, y) 1 c
More informationgrad φ(p ) φ P grad φ(p ) p P p φ P p l t φ l t = 0 g (0) g (0) (31) grad φ(p ) p grad φ φ (P, φ(p )) xy (x, y) = (ξ(t), η(t)) ( )
2 9 2 5 2.2.3 grad φ(p ) φ P grad φ(p ) p P p φ P p l t φ l t = g () g () (3) grad φ(p ) p grad φ φ (P, φ(p )) y (, y) = (ξ(t), η(t)) ( ) ξ (t) (t) := η (t) grad f(ξ(t), η(t)) (t) g(t) := f(ξ(t), η(t))
More informationI ( ) 2019
I ( ) 2019 i 1 I,, III,, 1,,,, III,,,, (1 ) (,,, ), :...,, : NHK... NHK, (YouTube ),!!, manaba http://pen.envr.tsukuba.ac.jp/lec/physics/,, Richard Feynman Lectures on Physics Addison-Wesley,,,, x χ,
More informationmain.dvi
6 FIR FIR FIR FIR 6.1 FIR 6.1.1 H(e jω ) H(e jω )= H(e jω ) e jθ(ω) = H(e jω ) (cos θ(ω)+jsin θ(ω)) (6.1) H(e jω ) θ(ω) θ(ω) = KωT, K > 0 (6.2) 6.1.2 6.1 6.1 FIR 123 6.1 H(e jω 1, ω
More information第1章 微分方程式と近似解法
April 12, 2018 1 / 52 1.1 ( ) 2 / 52 1.2 1.1 1.1: 3 / 52 1.3 Poisson Poisson Poisson 1 d {2, 3} 4 / 52 1 1.3.1 1 u,b b(t,x) u(t,x) x=0 1.1: 1 a x=l 1.1 1 (0, t T ) (0, l) 1 a b : (0, t T ) (0, l) R, u
More information振動と波動
Report JS0.5 J Simplicity February 4, 2012 1 J Simplicity HOME http://www.jsimplicity.com/ Preface 2 Report 2 Contents I 5 1 6 1.1..................................... 6 1.2 1 1:................ 7 1.3
More information29 1 6 1 1 1.1 1.1 1.1( ) 1.1( ) 1.1: 2 1.2 1.2( ) 4 4 1 2,3,4 1 2 1 2 1.2: 1,2,3,4 a 1 2a 6 2 2,3,4 1,2,3,4 1.2( ) 4 1.2( ) 3 1.2( ) 1.3 1.3 1.3: 4 1.4 1.4 1.4: 1.5 1.5 1 2 1 a a R = l a l 5 R = l a +
More informationI ( ) 1 de Broglie 1 (de Broglie) p λ k h Planck ( Js) p = h λ = k (1) h 2π : Dirac k B Boltzmann ( J/K) T U = 3 2 k BT
I (008 4 0 de Broglie (de Broglie p λ k h Planck ( 6.63 0 34 Js p = h λ = k ( h π : Dirac k B Boltzmann (.38 0 3 J/K T U = 3 k BT ( = λ m k B T h m = 0.067m 0 m 0 = 9. 0 3 kg GaAs( a T = 300 K 3 fg 07345
More information5. [1 ] 1 [], u(x, t) t c u(x, t) x (5.3) ξ x + ct, η x ct (5.4),u(x, t) ξ, η u(ξ, η), ξ t,, ( u(ξ,η) ξ η u(x, t) t ) u(x, t) { ( u(ξ, η) c t ξ ξ { (
5 5.1 [ ] ) d f(t) + a d f(t) + bf(t) : f(t) 1 dt dt ) u(x, t) c u(x, t) : u(x, t) t x : ( ) ) 1 : y + ay, : y + ay + by : ( ) 1 ) : y + ay, : yy + ay 3 ( ): ( ) ) : y + ay, : y + ay b [],,, [ ] au xx
More information2019 1 5 0 3 1 4 1.1.................... 4 1.1.1......................... 4 1.1.2........................ 5 1.1.3................... 5 1.1.4........................ 6 1.1.5......................... 6 1.2..........................
More informationr
73 29 2008 200 4 416 2008 20 042 0932 10 1977 200 1 2 3 4 5 7 8 9 11 12 14 15 16 17 18 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 200r 11 1 1 1 1 700200 200
More informationNo. 1261 2003. 4. 9 14 14 14 14 15 30 21 19 150 35 464 37 38 40 20 970 90 80 90 181130 a 151731 48 11 151731 42 44 47 63 12 a 151731 47 10 11 16 2001 11000 11 2002 10 151731 46 5810 2795195261998 151731
More information301-A2.pdf
301 21 1 (1),, (3), (4) 2 (1),, (3), (4), (5), (6), 3,?,?,??,?? 4 (1)!?, , 6 5 2 5 6 1205 22 1 (1) 60 (3) (4) (5) 2 (1) (3) (4) 3 (1) (3) (4) (5) (6) 4 (1) 5 (1) 6 331 331 7 A B A B A B A 23 1 2 (1) (3)
More information(iii) 0 V, x V, x + 0 = x. 0. (iv) x V, y V, x + y = 0., y x, y = x. (v) 1x = x. (vii) (α + β)x = αx + βx. (viii) (αβ)x = α(βx)., V, C.,,., (1)
1. 1.1...,. 1.1.1 V, V x, y, x y x + y x + y V,, V x α, αx αx V,, (i) (viii) : x, y, z V, α, β C, (i) x + y = y + x. (ii) (x + y) + z = x + (y + z). 1 (iii) 0 V, x V, x + 0 = x. 0. (iv) x V, y V, x + y
More information70 : 20 : A B (20 ) (30 ) 50 1
70 : 0 : A B (0 ) (30 ) 50 1 1 4 1.1................................................ 5 1. A............................................... 6 1.3 B............................................... 7 8.1 A...............................................
More information5 c P 5 kn n t π (.5 P 7 MP π (.5 n t n cos π. MP 6 4 t sin π 6 cos π 6.7 MP 4 P P N i i i i N i j F j ii N i i ii F j i i N ii li i F j i ij li i i i
i j ij i j ii,, i j ij ij ij (, P P P P θ N θ P P cosθ N F N P cosθ F Psinθ P P F P P θ N P cos θ cos θ cosθ F P sinθ cosθ sinθ cosθ sinθ 5 c P 5 kn n t π (.5 P 7 MP π (.5 n t n cos π. MP 6 4 t sin π 6
More informationchap03.dvi
99 3 (Coriolis) cm m (free surface wave) 3.1 Φ 2.5 (2.25) Φ 100 3 r =(x, y, z) x y z F (x, y, z, t) =0 ( DF ) Dt = t + Φ F =0 onf =0. (3.1) n = F/ F (3.1) F n Φ = Φ n = 1 F F t Vn on F = 0 (3.2) Φ (3.1)
More information