C:/大宮司先生関連/大宮司先生原稿作業用1/圧縮性流れの解法３.dvi
Size: px
Start display at page:

Download "C:/大宮司先生関連/大宮司先生原稿作業用1/圧縮性流れの解法３.dvi"

Transcription

1 8 aldwn-lomax hen 8. +ru = t (8.a) u+r(uu+) =r +f t (8.b) e +rhu = r ( u);r q+f u t (8.c) u e = (+u 2 =2) H = h+u 2 =2=(e+)= q f (8.) (comressble Naver-Stokes equatons) T h = += = RT d = c v dt dh = c dt c v c R = c =c v R = c ;c v c = RT M = juj=c (DNS, drect numercal smulaton) (vscous stress tensor) (heat ux) q j = ; u j +u j ; 2 3 ju k k ( j = 2 3) (8.2a) q = ;T = ; c 2 ( = 2 3) (8.2b) ; P r x u j = u j =x j P r = c = (Prandtl number)

2 2 8.. Naver-Stokes (ensemble-averaed Naver-Stokes equatons) (Favre mean) u u = u+u u = (8.3) u u u u = eu+u eu = u= u = ; u = (8.4) eu u u = u u = eu;u = u = eu = eu = u = u+ u 2 (8.) + ru = t u + r(uu+) =r + f t (8.5b) E + r(e+) u = r u ;rq + f u t (8.5c) (8.5a) u = u;eu = u; u = (u+u );(+ )(u+u ) = (u ; u )=u ; u a = a ab = a b eab = ea b f ab = a e b 2 eu = (+ ) u = u+ u = u

3 3 u = eu uu = (eueu+2euu +u u )= eueu + u u E = (+u u=2) = e + 2 eu eu + ] 2 u u E e (E+)u = (h+u u=2)u = E e u+eu+ e h u + u u eu+ ^ 2 u u u (ensemble-averaed Naver- Stokes equatons) + reu = t t eu + r(eueu+) =r( f ; u u )+f t E e + r(e+) e ; eu = r (f ; u u )eu ; q ; h u + f u u^ u u =2 3. (8.6a) (8.6b) (8.6c) (8.5) (8.6) (8.) j q j = ; u j +u j ; 2 3 ju k k ; u u j ( j = 2 3) q = ; c 2 + h ; P u ( = 2 3) r ;u u j = ; u u j (Reynolds stress) h u = h u (turbulent heat ux) 2 (8.) j q ) u ) eu e ) e E ) H ) e E+= (8.6) (8.) e e ) e E = ; e + 2 eueu + 2 u u 3. ; e h = e+ = f = f ; = = =

4 4 = R e T de = c v d e T d e h = c de T (8.7a) =~e =~ e E; f 2 eh = e E+ = e E; f 2 = ~ ( f c2 +f 2 ) (8.7b) (8.7c) ~ = ; f 2 = 2 ~(eu eu+ ] u u ) f c2 = Re T ec = q fc 2 ` ' ` e ' 8..2 Naver-Stokes (8.) (cartesan coordnates) x q t + F +D+ = x q = u u 2 u 3 e D = ; x F = 2 3 u u u + u 2 u + 2 u 3 u + 3 Hu = ; j u j ;q f u ( = 2 3) f f 2 f 3 (8.8a) (8.8b) q F D (eneral curvlnear coordnates) (8.) J Jr = J(r ) U = ur t J u + J e U uu +r = (Jr ) HU + J u;q u

5 5 ^q t + ^F + ^D+^ = ^q = J u u 2 u 3 e ^D = ; J j ^F = J j j2 j3 U u U + u 2 U + 2 u 3 U + 3 HU ^ = ;J jk u k ;q j f k u k ( = 2 3) f f 2 f 3 (8.9a) (8.9b) ^q ^F ^D ^ 4 J = (x y z)=( ) j = =x j (8.9) (8.8) x (8.9) (curvlnear coordnate rd) J 8. J = x x x y y y z z z (x ;x )(x ;x )(x ;x ) J x x = x x 2 = y x 3 = z = 2 = 3 = Jr Jr = J x J y J z = y y (x ;x )(x ;x ) z z x x! z z x x y y 6 : H Hj H HH 6 H H HH W U H H : Hj V : V U H H Hj H 6 H H HH H W H 8.:

6 6 Jr = const. x = const. (8.9) J U =const. Jjr j x U l u r l (8.b) Jr l Jr l u = JU l Jr l (ruu+) =r l J(U u+r )= J(U U l + l ) ; J(U u+r ) r l ^q t + ^F + ^D+^ = ~q t + F ~ + R+ ~ D+~ ~ = ~q = J U U 2 U 3 e ~ F = J ~R = ;J(U u+r ) ~D = ;J j x k = k j 2 3 u U U U + U 2 U + 2 U 3 U HU r r 2 r 3 ; J j k T j ( = 2 3) ~ = ;Jf r r 2 r 3 u (8.a) (8.b) (8.c)

7 7 (8.b) ~q F ~ R ~ D ~ ~ (8.c) u U j = k j k (a b)= = a b= (8.) (mass ux)ju JU x = const. 3 (8.9) 3 (8.) R ~ 8..3 aldwn-lomax hen 2 aldwn-lomax l ( ) hen k ; k aldwn-lomax (978) hen (982) 2 q j =(+ t ) u j +u j ; 2 3 ju k k ; 2 3 jk ( j = 2 3) (8.a) q = ; ; P r + t P rt c 2 x ( = 2 3) (8.b) t (eddy vscosty) k = u u =2 (turbulent knetc enery) P rt (turbulent Prandtl number) P r = :72 P rt =:9() =:5( ) (8.a) (8.b) (8.2a) (8.2b) t = (8.a) (Reynolds stress) t (8.b) (turbulent heat ux) ;T=x (thermal eddy vscosty) t = c t =P rt t 2

8 8 aldwn-lomax 2 t = ( (t ) nner (d d crossover ) ( t ) outer (d>d crossover ) (8.2a) d d crossover ( t ) nner =( t ) outer d Prandtlvan Drest ( t ) nner = l 2 jj (8.2b) l = df;ex(;y + = + ) = ru =:4 Karman + =26 y + = u d= w = w w d= w u = w = w w lauser ( t ) outer =:6KF wake F Kleb (d) (8.2c) K =:68 lauser F wake = mn ; d max F max :25d max u df 2 =F max F Kleb (d) = h :3d +5:5 d max 6 ; d max F (d) =d jjf;ex(;y + = + ) F max d ex(;y + = + )= u df = juj max ;juj mn juj mn = F Kleb Klebano ( t ) max < 4 (8.3) t = aldwn-lomax ( t ) max (8.3) (8.) aldwn-lomax (8.2) hen k ; y = const. hen t = c f k 2 = (8.4a) k ^q t t + ^F t + ^D t +^ t = (8.4b)

9 9 ^q t = J k ^ t = ;J! ^Ft = JU k! P ;;D k (c P ;c 2 f;f 3 D) ^Dt = ; J j (+ t ) k j + t j (8.4c) P = ;u u j u =x j ;u u j D =2k=d2 d c =:9 c =:35 c 2 =:8 =:3 f =;e ;c3y+ f =; :4 2 :8 e;(ret=6) f 3 = e ;c4y+ c 3 =:5 c 4 =:5 Re t = k 2 = Re t y + du = =4 k k k = = k ; k q 2 q 3 k P k k 3 k

10 8.2 k ; k k (lnearzaton) (daonalzaton) 8.2. k k (8.4) +ru = t (8.5a) u+r(uu+) = t (8.5b) e +rhu = t (8.5c) k +rku = t (8.5d) +ru = t (8.5e) q t + F x = ( = 2 3) (8.6a) 2 3 q F q = u u 2 u 3 e k F = u u u + u 2 u + 2 u 3 u + 3 Hu ku u 2 ( = 2 3) (8.6b)

11 F q df = F q dq = dq F = q d q = (8.7) (8.6) q t + q = x ( = 2 3) (8.8a) = F =q 5 = 2 3 ;u u + 2 D 2 u ; ~u 2 3 u ; ~u 3 ~ ;u 2 u u 2 ; 2 ~u D 2 3 u 2 ; 2 ~u 3 2 ~ ;u 3 u u 3 ; 3 ~u 2 u 3 ; 3 ~u 2 D 3 3 ~ ;Hu + 2 u H ;~u u 2 H ;~u 2 u 3 H ;~u 3 u u ;ku k 2 k 3 k u ;u 2 3 u (8.8b) D j = u + j (;~)u j ~ = ; 2 =~u 2 =2 H = e+ = c2 + 2 ~ = e ;2 (8.5) + ur + r u = t (8.9a) u t + uru+ r = (8.9b) t + ur + c2 r u = k + urk = t (8.9d) + ur = t (8.9e) (8.9c) q q t + = ( = 2 3) (8.2a) x 5 F q q

12 2 q = u u 2 u 3 k = u 2 3 u = u 2 = u 3 = c 2 2 c 2 3 c 2 u u u (8.2b) (8.2) dq = q dq = Ndq q (8.2) (8.8) N = N N ; q q q = Nq dnq = N = q =q N ; 6 N = N ; = ;u = = ;u 2 = = ;u 3 = = ~u 2 =2 ;~u ;~u 2 ;~u 3 ~ ;k= = ;= = u u 2 u 3 u 2 =2 u u 2 u 3 =~ k (8.22a) (8.22b) = N ; N = N ; R L N = R L (8.23) 6 N q q q

13 3 k L l k R = L; r k k l k ( ) k 7 j ; Ij = u ; 2 3 u ; = u ; 2 = u ; 3 = c 2 2 c 2 3 c 2 u ; u ; u ; = = u (5 ) 2 = u +c 3 = u ;c l k = u l ( ; I) =(l k l2 k = u c l ( ; I)=(l k l 2 k l7 k ) l 7 k ) 2 3 = 2 = 3 = c 2 2 c 2 3 c 2 c 2 3 c = c 2 = c 3 = c 2 2 c 2 3 c 2 c c = c 7 L u u +c u u ;c u k u L R L L L = L N =

14 4 R = N ; R = L = R = N ; u u + c u + 2 c u + 3 c u ;c u u ;=c 2 =c 2 =c 3 =c 2 3 ;=c =2c 2 =2c 3 =2c ;=2c ; =2 =2 ; 2 =2 2 =2 ; 3 =2 3 =2 c=2 2 c=2 3 c=2 ;c=2 N (8.24a) (8.24b) (8.24c) (8.2) L (8.6) L q L t + F = L q x t + L q = (8.25) x ; t +u ; ; x c 2 t +u = x n t +(u + j c) o u j + n j x c t +(u +c) o = (j = 2 3) (8.26) x n t +(u ;c) ou ; n x c t +(u ;c) o = x ; t +u ; k = x t +u = x dx =dt = u dx =dt = u +c dx =dt = u ;c =t+u =x =t+(u + c)=x =t+(u ;c)=x dx =dt = u dx =dt = u dx =dt = u +c dx =dt = u ;c dx =dt = u k

15 k t J + JU = t Ju + J(uU +r )= t Je+ JHU = t Jk + JkU = t J + JU = (8.27a) (8.27b) (8.27c) (8.27d) (8.27e) ^q t + ^F = ( = 2 3) (8.28a) ^q = J u u 2 u 3 e k ^F = J U u U + u 2 U + 2 u 3 U + 3 HU ku U ( = 2 3) (8.28b) ^F ^q j ^F ^q Euler d ^F = ^F ^q d^q = ^ d^q ^F = ^ ^q d ^ ^q = (8.29) (8.28) ^q t + ^ ^q = ( = 2 3) (8.3a) ^ = ^F = ^q ^ = 2 3 ;u U + 2 ^D 2 u ;~ u 2 3 u ;~ u 3 ~ ;u 2 U u 2 ;~ 2 u ^D2 3 u 2 ;~ 2 u 3 ~ 2 ;u 3 U u 3 ;~ 3 u 2 u 3 ;~ 3 u 2 ^D3 ~ 3 ;HU + 2 U H ;~U u 2 H ;~U u 2 3 H ;~U u 3 U ;ku k 2 k 3 k U ;U 2 3 U (8.3b)

16 6 ^D j = U +(;~) j u j ~ = ; 2 =~u 2 =2 j = =x j (8.9) ur = U = r = r = t + U + r u = (8.3a) u t + U u + r = (8.3b) t + U + c 2 r u = (8.3c) k t + U k = (8.3d) t + U = (8.3e) ^q t + ^ ^q = ( = 2 3) (8.32a) ^q = q = u v w k ^ = U 2 3 U = U 2 = U 3 = c 2 2 c 2 3 c 2 U U U (8.32b) (8.32) (8.3) ^q = ^q = N=J d^q =( ^q = ^q)d^q =(N=J)d^q (8.32) ^ ^ ^ ^ = N ; ^ N = N ; ^R ^ ^L N = ^R ^ ^L (8.33) ^ ^ = U (5 ) ^ 2 = U + c ^3 = U ; c j = k j k ^ ^ = U U + c U c U c U ; c U U (8.34a)

17 7 ^L = ^R = N ; ;=c 2 2 ; ; 3 3 =c 2 2 ; ; =c 3 3 ; ; =c 2 3 ; =c 2 2 c 2 22 c D 3 2 2; ; ; D ; ; ; c ; 2 c N D c 2 c 3 c ; c D j = 3 2 j; j 2 +(; j ) (j = 2 3) (8.34b) (8.34c) (8.28) ^L J ^q t + ^F = ^L ^q t + ^ ^q ^L = (8.35) t +U ; c 2 t +U = n +; U + t o n c U + +; U + c t o c = ( j = ) t +U u j ; j t +U u = ( j 6= ) (8.36) n +; U ; t o n c U ; ;; U ; c t o c = t +U k = t +U = d =dt = U d =dt = U + c d =dt = U ; c =t+u = =t+(u + c) = =t+(u ; c) = k

18 k t J + JU = t JU + t Je+ JHU = t Jk + JkU = t J + JU = J ; UU +(r r) = (8.37a) (8.37b) (8.37c) (8.37d) (8.37e) ~q t + ~ F = ( = 2 3) (8.38a) ~q = J U U 2 U 3 e k ~ F = J U U U + U 2 U + 2 U 3 U + 3 HU ku U ( = 2 3) (8.38b) ~F ~q d ~ F = ~ F ~q d~q = ~ d~q ~ F = ~ ~q d ~ ~q = (8.39) (8.38) ~q t + ~ ~q = ( = 2 3) (8.4a) ~ = ~ F = ~q ~ = 2 3 ;U U + 2 ~ D 2 U ;~ 2 3 U ;~ 3 ~ ;U 2 U U 2 ;~ 2 ~ D2 3 U 2 ;~ 2 3 ~ 2 ;U 3 U U 3 ;~ 3 2 U 3 ;~ 3 2 ~ D3 ~ 3 ;HU + 2 U H ;~ U 2 H ;~ 2 U 3 H ;~ 3 U U ;ku k 2 k 3 k U ;U 2 3 U (8.4b)

19 9 ~D j = U + j U j ;~ j j =(x k = )u k = j U j j =(x k = )(x k = j ) t + U + U = (8.4a) U t + U U + r r = (8.4b) t + U + c 2 U = (8.4c) k t + U k = (8.4d) t + U = (8.4e) ~q t + ~ ~q = (8.42a) ~q = U U 2 U 3 k ~ = U 2 3 U = U 2 = U 3 = c 2 2 c 2 3 c 2 U U U (8.42b) (8.42) (8.4) ~q = ~q = N=J ~ N ~ = J~q = ~q N ~ ; ~N = ~N ; = ;U = = ;U 2 = = ;U 3 = = 2 ;~ ;~ 2 ;~ 3 ~ ;k= = ;= = U U 2 U 3 u 2 =2 2 3 =~ k (8.43a) (8.43b)

20 2 d~q =( ~q = ~q)d~q =( N=J)d~q ~ ~ ~ ~ = ~ N ; ~ ~ N = ~ N ; ~ R ~ ~ L ~ N = ~ R ~ ~ L (8.44) ~ ~ L ~ R ~ = L ~ ; ~ = ^ ~L = ~R = ~ N ; ;=c 2 ; 2 2 = 22 ; 3 3 = 33 =c ; 2 = ; 3 23 = =c ; 3 = ; 2 32 = =c 2 3 ; =c =2 c 2 =2 22 c 3 =2 33 c ;=2 c ; =2 2 2 = =2 33 =2 2 =2 ; 2 = = =2 3 = =2 22 ; 3 =2 3 =2 c=2 2 c= c=2 33 ;c=2 (8.38) ~L J (8.45a) ~N (8.45b) (8.45c) ~q t + F ~ = L ~ ~q t + ~ L ~ ~q = (8.46) (8.36) k

21 2 8.3 Euler ourant FL =maxj t=x j = maxj^ t= j y + > 4 y + = 4 ourant (8.8) hen 2 (8.4) (delta-form mlct method) ni +t o ( n +D ) q n = rhs n (8.47a) x rhs = ;t F +D+ q n+ = q n +q n x ni +t o ( n x +D ) q (m) = ;(q (m;) ;q n )+ 2; rhs n +rhs (m;) (8.47b) q (m) = q (m;) +q (m) q = u u 2 u 3 e k D = ; x F = 2 3 (+ t ) k x + t u u u + u 2 u + 2 u 3 u + 3 x Hu ku u = ; ( = 2 3) f f 2 f 3 f u P ;;D k (c P ;c 2 f;f 3 D) (8.47c) (D q n )=x =x q n (8.47a) q n

22 22 (8.47b) t q n =(q (m;) ;q n )+q (m) q (m;) ;q n q (m) (8.) hen 2 (8.4) ni +t o ( ~ n + D ~ ) ~q n n = rhs (8.48a) rhs = ;t ^F + ^D+^ ni +t o ( ~ n + D ~ ) ~q (m) =~q (m;) +~q (m) ~q n+ =~q n +~q n ~q (m) = ;(~q (m;) ; ~q n )+ 2; rhs n + rhs (m;) (8.48b) ~q = J U U 2 U 3 e k ^D = ; J j ^F = J U u U + u 2 U + 2 u 3 U + 3 j j2 j3 jk u k ;q j HU ku U k j (+ t )k= k k j + t = k ( = 2 3) ^ = ;J f f 2 f 3 f k u k P ;;D k (c P ;c 2 f;f 3 D) (8.48c)

Similar documents

2019 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 information

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

II ( ) (7/31) II ( [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Re II 29 7 29-7-27 ( ) (7/31) II (http://www.damp.tottori-u.ac.jp/~ooshida/edu/fluid/) [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Reynolds [ (4.6), (45.8)] [ p.186] Navier Stokes I Euler Navier

More information

untitled

untitled 9 9. 9. 9. (FEM, nite element method) 4 9.. (element) (mesh discretization) DT LOK DT M([ ],[ ] )=[ ] DIMENSION M(,NF) DT M/,4,5,,5,,,5,6,,6,,,6,7, 4,8,9, 4,9,5,.../ DIMENSION M(4,NF) DO I=,IF- DO J=,JF

More information

Untitled

Untitled II 14 14-7-8 8/4 II (http://www.damp.tottori-u.ac.jp/~ooshida/edu/fluid/) [ (3.4)] Navier Stokes [ 6/ ] Navier Stokes 3 [ ] Reynolds [ (4.6), (45.8)] [ p.186] Navier Stokes I 1 balance law t (ρv i )+ j

More information

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

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 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 information

B ver B

B ver B B ver. 2017.02.24 B Contents 1 11 1.1....................... 11 1.1.1............. 11 1.1.2.......................... 12 1.2............................. 14 1.2.1................ 14 1.2.2.......................

More information

名称未設定

名称未設定 ! = ( u v w = u i u = u 1 u u 3 u = ( u 1 u = ( u v = u i! 11! 1! 13 % T = $! 1!! 3 ' =! ij #! 31! 3! 33 & 1 0 0%! ij = $ 0 1 0 ' # 0 0 1& # % 1! ijm = $ 1 & % 0 (i, j,m = (1,,3, (, 3,1, (3,1, (i, j,m

More information

‡ç‡¢‡Ó‡Ü‡Á‡Õ04-07„”

‡ç‡¢‡Ó‡Ü‡Á‡Õ04-07„”

More information

合併後の交付税について

合併後の交付税について (1) (2) 1 0.9 0.7 0.5 0.3 0.1 2 3 (1) (a), 4 (b) (a), (c) (a) 0.9 0.7 0.5 0.3 0.1 (b) (d),(e) (f) (g) (h) (a) (i) (g) (h) (j) (i) 5 (2) 6 (3) (A) (B) (A)+(B) n 1,000 1,000 2,000 n+1 970 970 1,940 3.0%

More information

Part () () Γ Part ,

Part () () Γ Part , Contents a 6 6 6 6 6 6 6 7 7. 8.. 8.. 8.3. 8 Part. 9. 9.. 9.. 3. 3.. 3.. 3 4. 5 4.. 5 4.. 9 4.3. 3 Part. 6 5. () 6 5.. () 7 5.. 9 5.3. Γ 3 6. 3 6.. 3 6.. 3 6.3. 33 Part 3. 34 7. 34 7.. 34 7.. 34 8. 35

More information

取扱説明書 ［F-02F］

取扱説明書 ［F-02F］ F-02F 4. 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 a b c d a b c d a b cd 9 e a b c d e 20 2 22 ab a b 23 a b 24 c d e 25 26 o a b c p q r s t u v w d h i j k l e f g d m n a b c d e f g h i j k l m n x 27 o

More information

000 001

000 001 all-round catalogue vol.2 000 001 002 003 AA0102 AA0201 AA0701 AA0801 artistic brushes AA0602 AB2701 AB2702 AB2703 AB2704 AA0301 AH3001 AH3011 AH3101 AH3201 AH3111 AB3201 AB3202 AB2601 AB2602 AB0701 artistic

More information

13 0 1 1 4 11 4 12 5 13 6 2 10 21 10 22 14 3 20 31 20 32 25 33 28 4 31 41 32 42 34 43 38 5 41 51 41 52 43 53 54 6 57 61 57 62 60 70 0 Gauss a, b, c x, y f(x, y) = ax 2 + bxy + cy 2 = x y a b/2 b/2 c x

More information

閨75, 縺5 [ ｨ ﾁ573, 縺 ｨ ｨ

閨75, 縺5 [ ｨ ﾁ573, 縺 ｨ ｨ 39ｨ 8 998 3. 753 68, 7 86 ﾀ7 9 9989769 438 縺48 縺55 3783645 ﾀ5 縺473 ﾀ7996495 ｨ 59754 8554473 9 8984473 3553 7. 95457357, 4.3. 639745 5883597547 6755887 67996499 ｨ 597545 4953473 9 857473 3553, 536583, 89573,

More information

HITACHI　液晶プロジェクター CP-AX3505J/CP-AW3005J　取扱説明書 -詳細版-　【技術情報編】

HITACHI　液晶プロジェクター CP-AX3505J/CP-AW3005J　取扱説明書 -詳細版-　【技術情報編】 B A C E D 1 3 5 7 9 11 13 15 17 19 2 4 6 8 10 12 14 16 18 H G I F J M N L K Y CB/PB CR/PR COMPONENT VIDEO OUT RS-232C LAN RS-232C LAN LAN BE EF 03 06 00 2A D3 01 00 00 60 00 00 BE EF 03 06 00 BA D2 01

More information

数値計算：有限要素法

数値計算：有限要素法 ( ) 1 / 61 1 2 3 4 ( ) 2 / 61 ( ) 3 / 61 P(0) P(x) u(x) P(L) f P(0) P(x) P(L) ( ) 4 / 61 L P(x) E(x) A(x) x P(x) P(x) u(x) P(x) u(x) (0 x L) ( ) 5 / 61 u(x) 0 L x ( ) 6 / 61 P(0) P(L) f d dx ( EA du dx

More information

i

i 009 I 1 8 5 i 0 1 0.1..................................... 1 0.................................................. 1 0.3................................. 0.4........................................... 3

More information

取扱説明書　-詳細版-　液晶プロジェクター　CP-AW3019WNJ

取扱説明書　-詳細版-　液晶プロジェクター　CP-AW3019WNJ B A C D E F K I M L J H G N O Q P Y CB/PB CR/PR COMPONENT VIDEO OUT RS-232C LAN RS-232C LAN LAN BE EF 03 06 00 2A D3 01 00 00 60 00 00 BE EF 03 06 00 BA D2 01 00 00 60 01 00 BE EF 03 06 00 19 D3 02 00

More information

(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y

(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y (2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = a c b d (a c, b d) P = (a, b) O P a p = b P = (a, b) p = a b R 2 { } R 2 x = x, y R y 2 a p =, c q = b d p + a + c q = b + d q p P q a p = c R c b

More information

1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載

1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載 1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載のない限り 熱容量を考慮した空き容量を記載しております その他の要因 ( 電圧や系統安定度など ) で連系制約が発生する場合があります

More information

(2016 2Q H) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y

(2016 2Q H) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y (2016 2Q H) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = a c b d (a c, b d) P = (a, b) O P a p = b P = (a, b) p = a b R 2 { } R 2 x = x, y R y 2 a p =, c q = b d p + a + c q = b + d q p P q a p = c R c b

More information

D v D F v/d F v D F η v D (3.2) (a) F=0 (b) v=const. D F v Newtonian fluid σ ė σ = ηė (2.2) ė kl σ ij = D ijkl ė kl D ijkl (2.14) ė ij (3.3) µ η visco

D v D F v/d F v D F η v D (3.2) (a) F=0 (b) v=const. D F v Newtonian fluid σ ė σ = ηė (2.2) ė kl σ ij = D ijkl ė kl D ijkl (2.14) ė ij (3.3) µ η visco post glacial rebound 3.1 Viscosity and Newtonian fluid f i = kx i σ ij e kl ideal fluid (1.9) irreversible process e ij u k strain rate tensor (3.1) v i u i / t e ij v F 23 D v D F v/d F v D F η v D (3.2)

More information

広報あぐい　2016年5月15日号

広報あぐい　2016年5月15日号

More information

HITACHI 液晶プロジェクター CP-EX301NJ/CP-EW301NJ 取扱説明書 -詳細版- 【技術情報編】 日本語

HITACHI 液晶プロジェクター CP-EX301NJ/CP-EW301NJ 取扱説明書 -詳細版- 【技術情報編】 日本語 A B C D E F G H I 1 3 5 7 9 11 13 15 17 19 2 4 6 8 10 12 14 16 18 K L J Y CB/PB CR/PR COMPONENT VIDEO OUT RS-232C RS-232C RS-232C Cable (cross) LAN cable (CAT-5 or greater) LAN LAN LAN LAN RS-232C BE

More information

u V u V u u +( 1)u =(1+( 1))u =0 u = o u =( 1)u x = x 1 x 2. x n,y = y 1 y 2. y n K n = x 1 x 2. x n x + y x α αx x i K Kn α K x, y αx 1

u V u V u u +( 1)u =(1+( 1))u =0 u = o u =( 1)u x = x 1 x 2. x n,y = y 1 y 2. y n K n = x 1 x 2. x n x + y x α αx x i K Kn α K x, y αx 1 5 K K Q R C 5.1 5.1.1 V V K K- 1) u, v V u + v V (a) u, v V u + v = v + u (b) u, v, w V (u + v)+w = u +(v + w) (c) u V u + o = u o V (d) u V u + u = o u V 2) α K u V u α αv V (a) α, β K u V (αβ)u = α(βv)

More information

LINEAR ALGEBRA I Hiroshi SUZUKI Department of Mathematics International Christian University

LINEAR ALGEBRA I Hiroshi SUZUKI Department of Mathematics International Christian University LINEAR ALGEBRA I Hiroshi SUZUKI Department of Mathematics International Christian University 2002 2 2 2 2 22 2 3 3 3 3 3 4 4 5 5 6 6 7 7 8 8 9 Cramer 9 0 0 E-mail:hsuzuki@icuacjp 0 3x + y + 2z 4 x + y

More information

Abstract :

Abstract : 17 18 3 : 3604U079- Abstract : 1 3 1.1....................................... 4 1................................... 4 1.3.................................. 4 5.1..................................... 6.................................

More information

1 8, : 8.1 1, 2 z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = n i=1 a ii x 2 i + i<j 2a ij x i x j = ( x, A x), f =

1 8, : 8.1 1, 2 z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = n i=1 a ii x 2 i + i<j 2a ij x i x j = ( x, A x), f = 1 8, : 8.1 1, z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = a ii x i + i

More information

http://www2.math.kyushu-u.ac.jp/~hara/lectures/lectures-j.html 2 N(ε 1 ) N(ε 2 ) ε 1 ε 2 α ε ε 2 1 n N(ɛ) N ɛ ɛ- (1.1.3) n > N(ɛ) a n α < ɛ n N(ɛ) a n

http://www2.math.kyushu-u.ac.jp/~hara/lectures/lectures-j.html 2 N(ε 1 ) N(ε 2 ) ε 1 ε 2 α ε ε 2 1 n N(ɛ) N ɛ ɛ- (1.1.3) n > N(ɛ) a n α < ɛ n N(ɛ) a n http://www2.math.kyushu-u.ac.jp/~hara/lectures/lectures-j.html 1 1 1.1 ɛ-n 1 ɛ-n lim n a n = α n a n α 2 lim a n = 1 n a k n n k=1 1.1.7 ɛ-n 1.1.1 a n α a n n α lim n a n = α ɛ N(ɛ) n > N(ɛ) a n α < ɛ

More information

repResultEndureTeam_for_TOTAL

repResultEndureTeam_for_TOTAL

More information

P MB-Z.indd

P MB-Z.indd エアシリンダ ø, ø, ø, ø, ø, ø 質量 New 16%削減 1.69kg RoHS ø-ストローク CJ1 CJP 従来品 2.01kg CM3 ロッドカバー ヘッドカバー 形状変更により質量削減 CG3 1 CS1 CS2 D- -X 技術 資料 383 øøøøøø MD D -Z- N V -M9W N 2 V 1 V1 W2 D2 T W 2 D2 N2 C1 G L V1 N

More information

(1) 1 y = 2 = = b (2) 2 y = 2 = 2 = 2 + h B h h h< h 2 h

(1) 1 y = 2 = = b (2) 2 y = 2 = 2 = 2 + h B h h h< h 2 h 6 6.1 6.1.1 O y A y y = f() y = f() b f(b) B y f(b) f() = b f(b) f() f() = = b A f() b AB O b 6.1 2 y = 2 = 1 = 1 + h (1 + h) 2 1 2 (1 + h) 1 2h + h2 = h h(2 + h) = h = 2 + h y (1 + h) 2 1 2 O y = 2 1

More information

2 Chapter 4 (f4a). 2. (f4cone) ( θ) () g M. 2. (f4b) T M L P a θ (f4eki) ρ H A a g. v ( ) 2. H(t) ( )

2 Chapter 4 (f4a). 2. (f4cone) ( θ) () g M. 2. (f4b) T M L P a θ (f4eki) ρ H A a g. v ( ) 2. H(t) ( ) http://astr-www.kj.yamagata-u.ac.jp/~shibata f4a f4b 2 f4cone f4eki f4end 4 f5meanfp f6coin () f6a f7a f7b f7d f8a f8b f9a f9b f9c f9kep f0a f0bt version feqmo fvec4 fvec fvec6 fvec2 fvec3 f3a (-D) f3b

More information

20 4 20 i 1 1 1.1............................ 1 1.2............................ 4 2 11 2.1................... 11 2.2......................... 11 2.3....................... 19 3 25 3.1.............................

More information

d bd o o p p i i u u j j du d f f g h h -

d bd o o p p i i u u j j du d f f g h h - - d bd o o p p i i u u j j du d f f g h h - 3 d p dp d 3 p -3 -4 -5 -6 u d d y f b d v p bd Uu XdXd Xd Xf Pp -7 h zj x j h 3 t y -8 -9 i id f d o p u i Wy Xd Ii r i v d -0 c c w r w q q q w q - - u u d

More information

50 2 I SI MKSA r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq

50 2 I SI MKSA r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq 49 2 I II 2.1 3 e e = 1.602 10 19 A s (2.1 50 2 I SI MKSA 2.1.1 r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = 3 10 8 m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq F = k r

More information

7 9 7..................................... 9 7................................ 3 7.3...................................... 3 A A. ω ν = ω/π E = hω. E

7 9 7..................................... 9 7................................ 3 7.3...................................... 3 A A. ω ν = ω/π E = hω. E B 8.9.4, : : MIT I,II A.P. E.F.,, 993 I,,, 999, 7 I,II, 95 A A........................... A........................... 3.3 A.............................. 4.4....................................... 5 6..............................

More information

(2) ( 61129) 117, ,678 10,000 10,000 6 ( 7530) 149, ,218 10,000 10,000 7 ( 71129) 173, ,100 10,000 10,000 8 ( 8530) 14

(2) ( 61129) 117, ,678 10,000 10,000 6 ( 7530) 149, ,218 10,000 10,000 7 ( 71129) 173, ,100 10,000 10,000 8 ( 8530) 14 16 8 26 MMF 23 25 5 16 7 16 16 8 1 7 16 8 2 16 8 26 16 8 26 P19 (1) 16630 16,999,809,767 55.69 4,499,723,571 14.74 9,024,172,452 29.56 30,523,705,790 100.00 1 (2) 16 6 30 1 1 5 ( 61129) 117,671 117,678

More information

25 7 18 1 1 1.1 v.s............................. 1 1.1.1.................................. 1 1.1.2................................. 1 1.1.3.................................. 3 1.2................... 3

More information

slide1.dvi

slide1.dvi 1. 2/ 121 a x = a t 3/ 121 a x = a t 4/ 121 a > 0 t a t = a t t {}}{ a a a t 5/ 121 a t+s = = t+s {}}{ a a a t s {}}{{}}{ a a a a = a t a s (a t ) s = s {}}{ a t a t = a ts 6/ 121 a > 0 t a 0 t t = 0 +

More information

取扱説明書［L-02E］

取扱説明書［L-02E］ L-02E 13.6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 a a a 35 a a a 36 37 a 38 b c 39 d 40 f ab c de g h i a b c d e f g h i j j q r s t u v k l mn op

More information

More information

A 2 3. m S m = {x R m+1 x = 1} U + k = {x S m x k > 0}, U k = {x S m x k < 0}, ϕ ± k (x) = (x 0,..., ˆx k,... x m ) 1. {(U ± k, ϕ± k ) 0 k m} S m 1.2.

A 2 3. m S m = {x R m+1 x = 1} U + k = {x S m x k > 0}, U k = {x S m x k < 0}, ϕ ± k (x) = (x 0,..., ˆx k,... x m ) 1. {(U ± k, ϕ± k ) 0 k m} S m 1.2. A A 1 A 5 A 6 1 2 3 4 5 6 7 1 1.1 1.1 (). Hausdorff M R m M M {U α } U α R m E α ϕ α : U α E α U α U β = ϕ α (ϕ β ϕβ (U α U β )) 1 : ϕ β (U α U β ) ϕ α (U α U β ) C M a m dim M a U α ϕ α {x i, 1 i m} {U,

More information

Sample function Re random process Flutter, Galloping, etc. ensemble (mean value) N 1 µ = lim xk( t1) N k = 1 N autocorrelation function N 1 R( t1, t1

Sample function Re random process Flutter, Galloping, etc. ensemble (mean value) N 1 µ = lim xk( t1) N k = 1 N autocorrelation function N 1 R( t1, t1 Sample function Re random process Flutter, Galloping, etc. ensemble (mean value) µ = lim xk( k = autocorrelation function R( t, t + τ) = lim ( ) ( + τ) xk t xk t k = V p o o R p o, o V S M R realization

More information

1 1.1 / Fik Γ= D n x / Newton Γ= µ vx y / Fouie Q = κ T x 1. fx, tdx t x x + dx f t = D f x 1 fx, t = 1 exp x 4πDt 4Dt lim fx, t =δx 3 t + dxfx, t = 1

1 1.1 / Fik Γ= D n x / Newton Γ= µ vx y / Fouie Q = κ T x 1. fx, tdx t x x + dx f t = D f x 1 fx, t = 1 exp x 4πDt 4Dt lim fx, t =δx 3 t + dxfx, t = 1 1 1.1......... 1............. 1.3... 1.4......... 1.5.............. 1.6................ Bownian Motion.1.......... Einstein.............. 3.3 Einstein........ 3.4..... 3.5 Langevin Eq.... 3.6................

More information

(5) 75 (a) (b) ( 1 ) v ( 1 ) E E 1 v (a) ( 1 ) x E E (b) (a) (b)

(5) 75 (a) (b) ( 1 ) v ( 1 ) E E 1 v (a) ( 1 ) x E E (b) (a) (b) (5) 74 Re, bondar laer (Prandtl) Re z ω z = x (5) 75 (a) (b) ( 1 ) v ( 1 ) E E 1 v (a) ( 1 ) x E E (b) (a) (b) (5) 76 l V x ) 1/ 1 ( 1 1 1 δ δ = x Re x p V x t V l l (1-1) 1/ 1 δ δ δ δ = x Re p V x t V

More information

K E N Z OU

K E N Z OU K E N Z OU 11 1 1 1.1..................................... 1.1.1............................ 1.1..................................................................................... 4 1.........................................

More information

構造と連続体の力学基礎

構造と連続体の力学基礎 II 37 Wabash Avenue Bridge, Illinois 州 Winnipeg にある歩道橋 Esplanade Riel 橋6 6 斜張橋である必要は多分無いと思われる すぐ横に道路用桁橋有り しかも塔基部のレストランは 8 年には営業していなかった 9 9. 9.. () 97 [3] [5] k 9. m w(t) f (t) = f (t) + mg k w(t) Newton

More information

http://www.ike-dyn.ritsumei.ac.jp/ hyoo/wave.html 1 1, 5 3 1.1 1..................................... 3 1.2 5.1................................... 4 1.3.......................... 5 1.4 5.2, 5.3....................

More information

b3e2003.dvi

b3e2003.dvi 15 II 5 5.1 (1) p, q p = (x + 2y, xy, 1), q = (x 2 + 3y 2, xyz, ) (i) p rotq (ii) p gradq D (2) a, b rot(a b) div [11, p.75] (3) (i) f f grad f = 1 2 grad( f 2) (ii) f f gradf 1 2 grad ( f 2) rotf 5.2

More information

all.dvi

all.dvi 5,, Euclid.,..,... Euclid,.,.,, e i (i =,, ). 6 x a x e e e x.:,,. a,,. a a = a e + a e + a e = {e, e, e } a (.) = a i e i = a i e i (.) i= {a,a,a } T ( T ),.,,,,. (.),.,...,,. a 0 0 a = a 0 + a + a 0

More information

n ξ n,i, i = 1,, n S n ξ n,i n 0 R 1,.. σ 1 σ i .10.14.15 0 1 0 1 1 3.14 3.18 3.19 3.14 3.14,. ii 1 1 1.1..................................... 1 1............................... 3 1.3.........................

More information

IA [email protected] Last updated: January,......................................................................................................................................................................................

More information

More information

(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

(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 [ ] 7 0.1 2 2 + y = t sin t IC ( 9) ( s090101) 0.2 y = d2 y 2, y = x 3 y + y 2 = 0 (2) y + 2y 3y = e 2x 0.3 1 ( y ) = f x C u = y x ( 15) ( s150102) [ ] y/x du x = Cexp f(u) u (2) x y = xey/x ( 16) ( s160101)

More information

海生研ニュース

海生研ニュース

More information

<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63>

<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63> 基礎からの冷凍空調 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/067311 このサンプルページの内容は, 初版 1 刷発行当時のものです. http://www.morikita.co.jp/support. 03-3817-5670FAX 03-3815-8199 i () () Q&A

More information

1

1 1 2 3 4 5 6 7 8 9 10 A I A I d d d+a 11 12 57 c 1 NIHONN 2 i 3 c 13 14 < 15 16 < 17 18 NS-TB2N NS-TBR1D 19 -21BR -70-21 -70-22 20 21 22 23 24 d+ a 25 26 w qa e a a 27 28 -21 29 w w q q q w 30 r w q!5 y

More information

KENZOU

KENZOU KENZOU 2008 8 2 3 2 3 2 2 4 2 4............................................... 2 4.2............................... 3 4.2........................................... 4 4.3..............................

More information

ae9 t Y Y v I o t y V U t y qv d, nfufil.lu9lfi1utia{'}un0a51.i nanls:?iln10{ila1?41il't5tru'tzua{1!fl0fit1nta{r,iltj't:?tlftl}.j1lljttfift{t!uzua.i't

ae9 t Y Y v I o t y V U t y qv d, nfufil.lu9lfi1utia{'}un0a51.i nanls:?iln10{ila1?41il't5tru'tzua{1!fl0fit1nta{r,iltj't:?tlftl}.j1lljttfift{t!uzua.i't ae9 t Y Y v I o t y V U t y qv d, nfufil.lu9lfi1utia{'}un0a51.i nanls:?iln10{ila1?41il't5tru'tzua{1!fl0fit1nta{r,iltj't:?tlftl}.j1lljttfift{t!uzua.i'tu 1$ ra n a 1 : uuu frr u ro n a r :d : v n a or

More information

Trapezoidal Rule θ = 1/ x n x n 1 t = 1 [f(t n 1, x n 1 ) + f(t n, x n )] (6) 1. dx dt = f(t, x), x(t 0) = x 0 (7) t [t 0, t 1 ] f t [t 0, t 1 ], x x

Trapezoidal Rule θ = 1/ x n x n 1 t = 1 [f(t n 1, x n 1 ) + f(t n, x n )] (6) 1. dx dt = f(t, x), x(t 0) = x 0 (7) t [t 0, t 1 ] f t [t 0, t 1 ], x x University of Hyogo 8 8 1 d x(t) =f(t, x(t)), dt (1) x(t 0 ) =x 0 () t n = t 0 + n t x x n n x n x 0 x i i = 0,..., n 1 x n x(t) 1 1.1 1 1 1 0 θ 1 θ x n x n 1 t = θf(t n 1, x n 1 ) + (1 θ)f(t n, x n )

More information

A

A A 2563 15 4 21 1 3 1.1................................................ 3 1.2............................................. 3 2 3 2.1......................................... 3 2.2............................................

More information

Fubini

Fubini 3............................... 3................................ 5.3 Fubini........................... 7.4.............................5..........................6.............................. 3.7..............................

More information

２０１２年１月号　０６１１５８／表２対向

２０１２年１月号　０６１１５８／表２対向

More information

22 25 34 44 10 12 14 15 11 12 16 18 19 20 21 11 12 22 10 23 24 12 25 11 12 2611 27 11 28 10 12 29 10 30 10 31 32 10 11 12 33 10 11 12 34

22 25 34 44 10 12 14 15 11 12 16 18 19 20 21 11 12 22 10 23 24 12 25 11 12 2611 27 11 28 10 12 29 10 30 10 31 32 10 11 12 33 10 11 12 34 22 25 34 44 10 12 14 15 11 12 16 18 19 20 21 11 12 22 10 23 24 12 25 11 12 2611 27 11 28 10 12 29 10 30 10 31 32 10 11 12 33 10 11 12 34 35 10 12 36 10 12 37 10 38 10 11 12 39 10 11 12 40 11 12 41 10 11

More information

p = mv p x > h/4π λ = h p m v Ψ 2 Ψ

p = 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 information

0.,,., m Euclid m m. 2.., M., M R 2 ψ. ψ,, R 2 M.,, (x 1 (),, x m ()) R m. 2 M, R f. M (x 1,, x m ), f (x 1,, x m ) f(x 1,, x m ). f ( ). x i : M R.,,

0.,,., m Euclid m m. 2.., M., M R 2 ψ. ψ,, R 2 M.,, (x 1 (),, x m ()) R m. 2 M, R f. M (x 1,, x m ), f (x 1,, x m ) f(x 1,, x m ). f ( ). x i : M R.,, 2012 10 13 1,,,.,,.,.,,. 2?.,,. 1,, 1. (θ, φ), θ, φ (0, π),, (0, 2π). 1 0.,,., m Euclid m m. 2.., M., M R 2 ψ. ψ,, R 2 M.,, (x 1 (),, x m ()) R m. 2 M, R f. M (x 1,, x m ), f (x 1,, x m ) f(x 1,, x m ).

More information

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

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 2.4 ( ) U(r) ( ) ( ) U F(r) = x, U y, U = U(r) (2.4.1) z 2 1 K = mv 2 /2 dk = d ( ) 1 2 mv2 = mv dv = v (ma) (2.4.2) ( ) U(r(t)) r(t) r(t) + dr(t) du du = U(r(t) + dr(t)) U(r(t)) = U x = U(r(t)) dr(t)

More information

( ) 5. VSS (VIM ) 10. ( ) 11. (ANN ) ( )

( ) 5. VSS (VIM ) 10. ( ) 11. (ANN ) ( ) 1.... ( ) 5. VSS.. 8. 9. (VIM ) 1. ( ) 11. (ANN ) 1. 1. ( ) 1 Lagrange 1..1 Lagrange q, Lagrange D(q)q + C(q; _q)_q + G(q) = (1.1) D(q)q C(q; _q)_q G(q) ( ) D(q) D(q) m ; M < M m (D(q)) (1.) (D(q)) M

More information

各位　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　平成１７年5月13日

各位　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　平成１７年5月13日 9000 1 6 7 8 8 9000 1960 1 2 2 3 3 1471 4 1362 5 2006 6 7 8 1967 9 1988 1988 10 1000 1348 5000 3000 2 11 3 1999 12 13 14 9000 A 15 9000 9000 9000 10000 16 6000 7000 2000 3000 6800 7000 7000 9000 17 18

More information
2026 © docsplayer.net プライバシー | 利用規約 | フィードバック