function solve_nonl_single11 D$ Q* E2 O& ]
clear all;clc K+ n" J1 Z( k/ ? z
format long
; f; |! L3 B" E0 r3 h; hglobal a
& s/ [- T& O+ O5 w u$ i. e, Ta_span=linspace(-0.06,0.06,200);* b) P* r) M/ j! H% A' `# Z$ a
n=length(a_span);2 F2 Z) i) } d* J3 n
x0=1e-9;
& z% Q2 n& O6 ~# r1 N2 K* \options=optimset('Algorithm','trust-region-dogleg','TolFun',1e-12,'TolX',1e-12);
& |" \ R1 q7 [for i=1:n/ h8 a- m2 Q+ T9 s1 ^* Y& z: ^- `, ~9 P
a=a_span(i);
9 \4 C K' v5 @; C6 A x(i)=fsolve(@nonl,x0,options);
8 ]' R. N9 j- ~ w0 ~ y(i)=nonl(x(i));
5 i- E. t, _$ r% _- I( `" l: Y) Q) p+ Cend
! {, s+ P u4 `. @. x3 ka_span', x',y'- F0 v$ r8 \. Y+ y8 E6 V
function f=nonl(x)7 _1 A& z- l7 R& @7 u B& }0 y
global a
! M- T5 _) d" F% O( U; Zf=1/2*(285+60)*3000*sin(x)-1/2*(25*sin(x)*sin(a)+(60-25*cos(x))*cos(a))*3000*sin(x)+60^2*25*sin(x)*a*sin(a)-60^2*25*cos(x)*a*cos(a)-60*285*(25*cos(x)*sin(a)+25*sin(x)*cos(a));" W" `. |" p" g
0 T) V$ ~. w0 O* k4 f運行結果 ans =
, J4 Z1 x0 [1 x -0.060000000000000
1 g& _( F$ C2 S3 F -0.059396984924623
Z" h# |1 }# X' J9 u+ f -0.058793969849246! x; ^; b8 c; J
-0.058190954773869
2 w' d/ h3 C" E: [" n6 w I0 Q -0.057587939698492
1 L( v! `7 U3 c/ c4 `3 | -0.0569849246231164 Y4 h5 a2 ?. w1 n# ^/ h6 ~
-0.056381909547739
- a+ c* o! |1 {' O& b" p -0.055778894472362
W- b% X0 K2 O7 r6 F -0.0551758793969852 i1 n' N1 ^5 s$ x& c0 `6 B8 Q
-0.054572864321608
) j h, v5 J5 x7 \4 [ @# K4 S -0.053969849246231
) g. W- o% K; f: K0 H$ C& M -0.053366834170854, n1 W& B: Z! e( t) `
-0.052763819095477
$ J9 B( B! Z: g9 C) c" w6 S7 l -0.052160804020100
0 e" C9 x c* Z) x. U6 v; ]2 x -0.051557788944724
# G" R r! I" c; S# p -0.050954773869347
" g( b P+ t' X9 _9 A' E/ I -0.050351758793970
( S3 H! g. p1 q7 N+ J. E9 r -0.0497487437185939 z$ ~! H; {4 H+ R# L
-0.049145728643216
6 X5 I) k* f6 O1 t8 T1 B -0.048542713567839! m. s1 C7 _, A5 q# z" d) n- B/ \
-0.047939698492462
+ e% ? Y! \# z G. K -0.047336683417085
) O/ B) f5 _0 c: | -0.046733668341709
: V0 e, d, x. i* M -0.0461306532663321 G2 @9 v. K* u2 O% t
-0.045527638190955
) `4 I4 |3 k# Z3 i0 j9 r! B -0.044924623115578: F! J) m+ c8 x0 d& b2 D) j
-0.0443216080402017 y. g+ N q$ s/ Q
-0.043718592964824
% m0 h" ?6 A- T% D& Q -0.043115577889447, w$ t+ e8 o* w6 O
-0.042512562814070& A: l# D0 s" S" V& u
-0.041909547738693* J# q: `* v1 ~7 y+ L7 J& v' p
-0.0413065326633178 U/ N' _, [2 W. D! T
-0.040703517587940
9 X* q7 V9 K; J# b c -0.040100502512563
4 S+ {. B- `+ g! ~ -0.039497487437186
. |. P9 R u$ k2 M6 a# b -0.038894472361809
/ H) c. A& H; ^; Y2 S; t- ~; z -0.0382914572864322 a+ ]: S" L' F
-0.0376884422110555 [/ l% U% _ A4 @+ e) Q1 ^, @
-0.0370854271356783 Z2 F1 h* f# H7 C
-0.036482412060302
7 u1 j4 @3 O) L! c9 J! p% X* W+ _7 o -0.035879396984925
: V9 O- w. V! J' d+ Z3 Y) i -0.035276381909548
; A* U: W9 o! g ?2 a( b -0.0346733668341712 O" m" S; U( Q& L7 ?
-0.034070351758794$ _+ _: J/ Q0 |+ I7 B) B' J: \
-0.033467336683417
5 a; E7 l; _: a0 Q) ^ F/ } -0.032864321608040
7 @& T5 `" A% I( B' w -0.0322613065326637 M( n" X u% S+ ?! _
-0.0316582914572861 v% Q- {: `8 v7 _8 \3 p) C* i
-0.031055276381910/ q" g# ?+ S3 V5 U5 d# b
-0.030452261306533
' L- x2 e( z. a/ T/ ^ -0.029849246231156$ w ^8 D9 s& V R
-0.029246231155779
. ^( `+ N( o6 k4 O5 ? -0.0286432160804022 D" e4 G# d0 a( j4 b% L- m
-0.028040201005025; o% I! P; B8 }% R+ r* G; ?& H
-0.027437185929648/ v; n4 M2 {4 _) F, u
-0.0268341708542714 T/ b$ e6 W+ T2 V; ]
-0.026231155778894. n$ W% B0 {! y6 h* A3 v1 m/ r
-0.025628140703518/ a) W- q% b) M, B2 o4 p" a
-0.025025125628141
- a% U" F( l; b$ M' N1 m+ a -0.024422110552764
5 { }+ v- c0 @( ]. m -0.023819095477387
3 v# Z: R- Z! o# Q/ M, l' Q" f -0.0232160804020106 Q0 r/ ?# D: g* F, {* \+ \
-0.022613065326633
) y% `- a- V) l# S0 \. ? -0.0220100502512560 W! J4 f8 g6 f; S C D
-0.021407035175879
# u( I8 W. I4 u% T4 r6 m -0.020804020100503
) ~9 E2 C4 s+ V, m9 ^ A- Z- t -0.020201005025126
$ T) S; O# U/ k; M -0.019597989949749) _* ]% D C6 B& [+ O3 h
-0.018994974874372
, X" m8 _# m% Z -0.018391959798995
# `8 F$ V/ l: j+ E8 e" ] -0.017788944723618. s+ A" c, ]7 c0 a" s
-0.017185929648241
! K4 q# Y+ j& _9 S& \% k -0.016582914572864
. j1 Q2 G/ `0 D' W3 v4 C -0.0159798994974874 v- e) j/ ~/ H7 B
-0.015376884422111
7 d2 H7 f5 H+ S- k! M. z -0.014773869346734: O* C0 ]2 g; \% Y$ n1 {: P& Z9 B1 W
-0.014170854271357 [+ B/ T, ~$ F2 J
-0.0135678391959803 H9 S' B% B+ E8 \0 T
-0.012964824120603
) r: ?3 J6 ]# t1 V- G' U) ~/ j -0.012361809045226- }2 O$ ^5 F; m$ \& a- ]4 _* p
-0.0117587939698499 n$ K, u" ^7 F* w0 Q
-0.011155778894472
* a; V5 S$ _5 Y+ @ -0.010552763819095
O7 \( e, \7 ?9 J7 J& p/ I- L -0.009949748743719" a( U1 v8 @1 X9 d: ?: P. [( R
-0.009346733668342$ L3 Z- J- k2 |4 n
-0.008743718592965
8 K2 R& I9 J* U% N -0.0081407035175889 L" }1 L9 `. [* a! N
-0.007537688442211
4 I" [6 B) k0 e; B8 [ -0.006934673366834) J. u! k' o, P& r3 L1 ~
-0.006331658291457
4 f1 O9 }: g' ?$ R -0.0057286432160809 {; Y; q2 G3 ~: u4 O# W
-0.005125628140704# f: [1 c, W$ U) X
-0.0045226130653277 H% y7 c$ x K
-0.003919597989950) b% u! i' T, n {0 Q% }: d( r
-0.003316582914573: M, k: P8 P$ R; q
-0.002713567839196
B1 Z. O; Z2 x1 t% G% q -0.002110552763819
! R/ N+ U' i f: A -0.001507537688442% `, i! d! q2 h6 M
-0.000904522613065
3 o& W/ |' J' G9 N/ C0 I -0.000301507537688
* T2 v- P" U; L 0.000301507537688
* N: p" v- e2 } 0.000904522613065
' D# P$ e A+ {: ~ 0.0015075376884424 Z. M6 d6 l7 K1 b2 W
0.002110552763819
: j6 A k8 M" i# ?. O4 ]" y" I 0.002713567839196* Z9 Q) y/ ^( Y8 e. f$ S
0.003316582914573. [/ ~7 S$ h1 }
0.003919597989950- U! b; U) p( Q
0.004522613065327! r, v9 e7 O, g7 n6 o' G
0.005125628140704
$ g( u ], D$ i( O% w! O" q/ t& i 0.005728643216080
* y7 \+ }( `- n% T8 L4 p; r 0.0063316582914572 v2 G2 i& z n7 `6 o
0.006934673366834. o9 C3 y# z# `9 `) X8 H& F3 ~
0.007537688442211, g9 j# }. h3 S7 {
0.008140703517588
$ A7 p" ?2 [3 g& [ 0.008743718592965
! w" H# x! ~9 _2 R/ z+ o3 B" u 0.009346733668342, A) N- b1 u4 ?0 W S$ e, u
0.009949748743719
) E2 }) r/ y( q& R 0.010552763819095$ @$ v9 x$ j, M* j4 D1 a4 \
0.011155778894472- v) H: k5 I. q
0.011758793969849
) e o6 c& r( @. E/ U4 s2 K7 o 0.012361809045226. M. `) q* ^$ f- N9 i! t2 a
0.012964824120603" k0 g9 y. W& M# j8 s4 p8 V- @
0.013567839195980. R3 |' m2 u. a
0.014170854271357
1 m, a3 H! Y2 Y0 ^' T$ n+ A5 p 0.014773869346734+ d- w" m4 ~$ d3 r. E
0.015376884422111, X0 v. O8 u( i: L; c
0.015979899497487
. f/ Y0 |2 E5 P3 @ 0.016582914572864
5 l5 b' F4 `) x8 _1 A2 N 0.017185929648241- ?2 X8 \& j! G- i! Z3 \
0.017788944723618
7 C1 e. E1 Z: B2 W. p: O2 ^) w: t 0.018391959798995$ a; U7 J% e$ _9 I) |. R
0.018994974874372
5 o; g1 m" }! H, ^) y) e) \ 0.019597989949749
2 O& f* D2 T2 c 0.020201005025126) l# P. p& ?0 _4 O: f% N
0.020804020100503
* y; q) ~# o) M4 o; \ 0.021407035175879
4 M8 U3 N0 X8 ^. U 0.0220100502512561 J' [( C- y9 Z- M$ J- C7 Q
0.022613065326633
5 @3 H* Q7 C& E6 Q2 J& r 0.023216080402010, ]# u* G7 J* N: t0 n
0.023819095477387/ K: F* Y; v4 j. P7 k5 I1 ^+ v$ _
0.024422110552764. S. ]9 U: P3 g: _* }; L
0.025025125628141
- Q) s4 s* Z- J4 B* u+ p, N 0.0256281407035185 f# m, i- W( ~% W0 F
0.026231155778894 x* M) B: R9 ]; z! B P7 B O% h
0.026834170854271$ R5 l( L5 g& A% X: @5 F
0.027437185929648
/ b/ K+ [/ D/ A' ~; q. f3 @, B* d 0.0280402010050258 y% s) Q3 a4 B4 t8 l. R
0.0286432160804028 w1 r& ]& {: ?7 w" A V
0.029246231155779
& @: K% H$ N. ` 0.029849246231156; u1 n! O$ o* n$ ? C; P7 c
0.030452261306533$ s7 @$ }0 L9 `2 G( F- V2 C# F
0.031055276381910
/ v8 `- q( ^/ s$ ~* | 0.031658291457286
+ ^" a0 e: F6 B+ F# b' Z; w 0.0322613065326630 i a% a- p% K
0.032864321608040
+ x) \( W* E; J* l: r 0.0334673366834173 o8 t- E' n) C- ~
0.034070351758794! j0 o. Q% l1 P+ O: v% q
0.034673366834171
7 C. }+ Q5 }" W1 \ 0.035276381909548
! i8 L& q0 ]1 h& @ 0.035879396984925% v5 Q; \% G% {) q( m
0.036482412060302
4 m9 d1 l7 o* \0 G2 h3 e 0.037085427135678
* l; a. M, b# v& C- D 0.0376884422110557 W) T7 I* q+ L; L$ o7 l7 y0 M0 @
0.038291457286432
& ` v" k$ {. _2 Y$ Y 0.038894472361809% r- B2 w- I" W! m& c. X/ B1 z7 n; t# b
0.039497487437186. x& b: w% e C4 |: ?' E) u5 _* O& O
0.0401005025125638 {0 m2 ?2 ]* V: e& U& H
0.040703517587940
9 Q) S/ t( V2 G8 a" ~5 {* @ 0.041306532663317
$ m/ ~" r/ ]! i2 n0 a0 L- x 0.041909547738693
7 D2 F# }& c( R5 v7 `- |) C# z" T 0.042512562814070
% O# b% {- ^4 f% U, ]( n 0.043115577889447. I, T9 @. f w) o7 l
0.043718592964824
+ V/ f) a& h+ \7 m$ R- [ 0.044321608040201- p9 L" c A5 K" g' E4 t2 _* j
0.044924623115578
4 Q( C! h5 o3 f5 i 0.045527638190955! ?9 p( O) ?( y* T
0.046130653266332$ a- }! m" [8 U! A3 f' V6 K m
0.046733668341709
' J+ z- K1 I8 ?; ]4 O6 y: t* a 0.047336683417085
. |% H0 D J; v 0.0479396984924623 E7 b9 F0 i: h' ]
0.048542713567839! I- b( b% y$ G# w/ Z
0.049145728643216- [1 L) X5 G j, ? R4 T" h
0.049748743718593
6 u8 X7 L$ B8 E; k; e3 ~: L 0.050351758793970+ J! {0 L6 r9 R6 W
0.050954773869347
9 i' L5 @# s# {; [) A( ~2 h, W 0.0515577889447247 H+ z; A( n8 S" i
0.052160804020101) ^2 V3 t" X6 m1 V# [
0.052763819095477
& z1 T/ b1 q' v! W& z- _ 0.053366834170854
, _( r, W# n! I+ S 0.053969849246231
1 R" L. j( ^$ ~3 b. } 0.054572864321608# Y! C/ A: W5 j6 T
0.055175879396985; A2 r, `/ _( T) Z+ x- t1 G" n
0.055778894472362) X* M# ]1 P. {( U
0.056381909547739) _7 E" m- W7 {( L) n) D6 R6 N6 o [7 e
0.056984924623116
& J0 C9 ?0 W7 N9 L/ v 0.057587939698492
+ j& F3 D+ U. v9 ] 0.058190954773869
& g$ f) t6 b0 q; _* E 0.058793969849246. s& i2 D7 ]2 w6 a
0.059396984924623. s. M/ g1 E. p! |/ }1 A. N
0.060000000000000 m! J2 `" x2 W7 s, a3 C7 C- T
8 v( _( Q% B+ @9 l* ^% G4 \
! i, |5 G( J6 Q8 A
ans =
0 t4 X4 b; Z+ `# L8 C) {7 R2 J& i( ~) D* ~. c, W2 t8 u9 x, i
-1.033689540653716
! K1 ~) K% u6 P* _( } -1.013619827890691
8 j$ ^( X* O& ~8 | -0.9946213665310836 v) y( _. i4 ?% q3 S
-0.976510534039504
. ^$ u3 Z& x+ t4 _ -0.959151639002957% ?2 P' _8 `1 F2 r8 |1 q% ?
-0.942440908631668
O" q* I- J3 d1 c& k) k; h -0.926296779035772
- ]6 u' N' f4 A# D -0.910653694311287
; p$ K2 v, z, I0 ] u6 Q1 h. } -0.895457976752101. F) s0 Y7 ?' Q& V4 E' X
-0.880664979264975
9 i$ E& Z5 X( d: g y! D+ U -0.866237063671064
( ?4 l& L# P9 q6 q8 S/ F -0.8521421291006716 i% I$ J2 g5 b7 M# m
-0.8383525174605603 O, \# _ k( f
-0.8248441838903396 M1 ]* C$ Y5 r5 t) V, O# `
-0.811596057546419
0 l4 P/ I8 n2 _! o -0.798589541746273
4 H8 y, x& K- { -0.785808117918193
, @$ g% {9 L$ D7 a -0.7732370280687399 l* x. `1 @8 t' \( G, Z+ N5 [
-0.760863017467603
I. @' `/ f" v! c0 L8 R -0.748674124097121
5 `* X/ I/ c' a -0.736659504835453
3 ^2 U K3 a0 O- ^2 V -0.724809290796292! F' P& \8 {& d: s, l# l0 f$ p
-0.713114466033284
1 i* {6 a3 y9 B+ J8 K- Q! ] -0.701566765133452
; [" ` s6 ?3 u% A" y3 M -0.690158586205827- c4 H. N2 w. m8 M5 o/ ?
-0.678882916512848
; X, {+ C/ L) M, J7 c -0.667733268556930
6 M6 u7 m. n' j; r -0.656703624869929
4 D8 N. h6 n) U4 U+ n: N -0.645788390090937+ d' f) c6 M# Y! S% ^+ k$ W
-0.634982349182892$ z- K' P) q% q/ o, x- h9 Q
-0.624280630847343% v n: u; g: X0 J
-0.6136786753631127 N) I% a# L; r% t
-0.603172206207723, k! ~1 [ A( e5 X
-0.592757204927887
- d; c0 P6 w+ {8 A4 h* W -0.582429888812360
. \9 k2 f! _% X7 d2 \7 W# { -0.572186690991612
, A" ^9 B( _% u. W4 F) Y3 ^' o -0.5620242426469659 j/ ]) y0 A# Y4 J1 P
-0.551939357060015
; b1 L. T$ L! V9 }: s+ W6 x7 } -0.541929015272840
/ w* M$ F" Q' @2 i# u8 i -0.531990353162879
8 R4 F! E$ L' H* G -0.522120649763841$ ~1 M6 i O+ P5 ]$ x8 h H+ T, v
-0.512317316687512
1 z" u( c3 L+ J4 ?4 f, Y# Z -0.502577888520921' q$ I6 k0 w# z d7 F: I: c
-0.492900014089836
( i @) I. f$ o -0.483281448493885
; p+ S7 f6 [* K) d) ~! D+ k -0.473720045830499
1 \* A( ~! a; ^+ Q3 x- b! b -0.464213752535263
) w' v* r3 J6 D/ B' d* ~# L -0.454760601275071
8 ]2 Y- a2 E& m2 f4 `* \ -0.445358705338140# D2 f5 l+ @' N1 Z
-0.4360062534714717 A* {7 n( J) u. L2 {" |% p
-0.426701505122098# z- H; X! A, {4 C0 Y
-0.417442786043397
: M' v$ @9 K: g: E& {3 k% Q -0.4082284842319928 i c1 M( V' Z
-0.399057046164675
: I/ O7 x2 F1 ` -0.389926973307911
, J1 h- X* |$ H4 p* G -0.3808368188754998 r" n( s' e: \1 {$ \: ^2 q" T1 y# S+ @
-0.371785184812454
1 }2 h3 m+ s2 }% g5 [# L3 a( f X3 c -0.362770718985392# x" b* Y7 }6 ~" z4 ?3 p( A1 Z6 s
-0.353792112561766/ D4 ?; V5 o1 O5 W" g
-0.3448480975619348 [, j# ~. \# Y' `
-0.335937444569670# v2 N! c# N) O) Y9 h1 s
-0.3270589605881063 a8 p; I5 B1 b& K
-0.318211487029265/ ~! P& I2 T! ?0 \
-0.309393897826506* C9 F- v- S- q j
-0.300605097660121
# a1 R! b, n2 A' [- g( j1 n e -0.2918440202872461 e" P9 ?3 R! ?/ p- D' F6 s7 }
-0.283109626967980. C/ @! \- k2 Y% i( M7 J& X6 _
-0.2744009049803694 |* S) C6 C% d
-0.2657168662174765 B7 ~! h) c' a
-0.257056545860381; K* b2 B" V; D7 v* G
-0.248419001121443
- B6 K+ |; D& f8 C. v -0.2398033100525972 R: U; O" Q# Q( p+ D
-0.2312085704139355 p* N0 [9 x# M0 A. {1 `3 p9 |
-0.222633898598121
: s3 T3 Q& F, r' p& y J -0.214078428606594
# k; C3 d: U$ T -0.205541311073791* ~1 d9 }7 j+ r/ a3 Z1 A( g
-0.197021712335900
) _8 G+ B% ~$ O1 n) y, I+ p' b6 { -0.188518813540922' T9 A$ ]! i0 k! T
-0.180031809797061; O8 z. Q' X: {, _# R
-0.171559909356608 M0 r& [5 f/ m$ L, h% j9 O9 s& v
-0.163102332832782
7 _/ V7 o, P9 O4 A# ]* {. [ -0.154658312447061! W* d8 b3 S$ E# P7 N, j) W
-0.146227091304754' D0 n0 Q+ D' |- I
-0.137807922696691
5 E( K$ |; f4 H+ \ -0.129400069425041. F3 k; o/ n7 ~, i6 v) v% v
-0.121002803151371( i5 h8 ?# B6 N- ^- f( C
-0.112615403765200
* Z4 P# J' K' |, I( q; ] -0.1042371587713620 k% W' Z ?& b0 F" R0 }
-0.095867362694613
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7 B+ i0 p7 g" o- x
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樓主: shouce
