function solve_nonl_single1
$ D5 d# G* ~9 R# ]clear all;clc! Q% ]2 @( [8 n2 u
format long
' w/ Y1 X5 U+ w" wglobal a
6 L9 N* u* x3 \2 v+ U8 Ua_span=linspace(-0.06,0.06,200);7 n6 O$ h; ^3 X7 r
n=length(a_span);
$ D; c3 Q( n" Y/ tx0=1e-9;
2 l. f4 ~ T' Y Noptions=optimset('Algorithm','trust-region-dogleg','TolFun',1e-12,'TolX',1e-12);
" e+ }2 m8 `. c( V( j( a) M* J6 V. Nfor i=1:n
2 V/ y# p6 C& G! w( I( M) M F! b a=a_span(i);5 h3 X! f& Z/ W+ V4 n
x(i)=fsolve(@nonl,x0,options);' Q! ~' E" r- [7 X4 ]# J A! \7 f/ ]' h
y(i)=nonl(x(i));; _/ K( h# M+ k) `) |+ Z5 g
end
0 l7 V$ b' V6 J: V& q" Oa_span', x',y'6 o/ _; f; u' K: h2 I9 g& ^( @1 K% [& v
function f=nonl(x)
+ a+ e9 h7 s5 _; w1 Aglobal a9 q8 E7 O0 J$ f3 }+ ?- V& \% ~
f=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));
! `6 B3 A, q# L, n7 z) L; Q! `$ U& x5 `6 f0 S
运行结果 ans =. ?/ T! L. [" [/ V' c8 u- u, \' I
-0.060000000000000
4 n# x9 q6 U8 |( w% P: ^ -0.059396984924623
8 o/ e6 p( w* U -0.058793969849246
+ ]7 R' |5 R0 j" b0 |' d; P -0.058190954773869& `' R/ T' f; f u
-0.057587939698492
! M1 t8 y2 k& f! | -0.056984924623116
9 B4 s' m0 f( G2 p' { A) R/ w, i -0.056381909547739
( r7 b( c3 q8 v( `: d( F. @ -0.055778894472362
D O) G/ v! {+ A -0.055175879396985& O5 M/ \/ h" {) \+ Q1 y+ m S3 c) W
-0.054572864321608" m) `+ N0 S/ z2 ^8 w- J) ]
-0.053969849246231
7 ]% A. s" ^ u& O4 t% u9 q -0.053366834170854
0 a, U. S0 N+ c6 P -0.0527638190954770 r0 Q1 V3 M" \5 y, L+ ~( t2 R- `
-0.052160804020100
& @# T3 |& S% l6 V9 S -0.051557788944724
2 W2 A5 B# [1 s, V% O p. H- K. ~+ p -0.050954773869347" V0 _# o$ l5 E/ f y& m/ y
-0.050351758793970
2 g1 F# Z2 U' @8 S1 u7 ~ -0.049748743718593' }/ o: ?% r+ u5 O8 l! _. H
-0.049145728643216
7 n5 Q5 z: ^; x0 q -0.048542713567839
# t: m( H! |2 x' E -0.047939698492462- l1 p% L. {. L; w5 }
-0.047336683417085
& I6 T7 j; I" m- d -0.046733668341709) Q6 u3 M! y6 L, K4 i& }
-0.046130653266332+ B% `7 r( \' Z: }: Y5 C! N# W- p& E5 Y8 e
-0.0455276381909557 y5 s5 A& I ?* J
-0.044924623115578
* M2 [' q3 }& O -0.044321608040201
8 R. `8 M# `7 ^7 D2 ? -0.043718592964824
, n H3 k' A v8 k -0.043115577889447) y* U" z" q- x$ v- O! {
-0.042512562814070: x3 C t2 }* {* D% j& l
-0.041909547738693
& q w- v3 k' S5 Z -0.041306532663317
4 b- ?/ n) e: O6 m" c3 p x: p, ?% O -0.040703517587940
$ f; I/ H/ O* P! N4 s -0.040100502512563
8 G! {9 T) L! I9 { -0.039497487437186
9 r: w, P7 S2 C$ C -0.038894472361809
; W! k- b7 _; h3 E- _7 | -0.038291457286432$ o7 M" [8 x' r1 ?; R) W) @2 p' l
-0.037688442211055) H/ @& o" c" J( B9 ~" u
-0.037085427135678
: Q* R Z! K8 J9 ^9 Q- n: x -0.036482412060302
9 J+ v1 Y) G, U2 i( t$ m( T -0.035879396984925! e3 w3 [3 \& T
-0.035276381909548
$ c1 K6 J- @ w2 z# Y7 c* K -0.0346733668341711 q- V7 v' x% {8 w2 U \: B
-0.0340703517587946 O, T" |* M4 n! g1 b
-0.033467336683417
; i2 }4 ~+ B3 R$ f -0.032864321608040& e3 S' ]) ]. K: R/ K& Y9 I
-0.032261306532663. t& |. R/ I# K7 H% A
-0.031658291457286) p0 i1 Y' Q8 v! V) o) |6 o
-0.031055276381910
. X, f% |/ {- w* N -0.030452261306533
$ t+ _5 O3 y9 {4 Y( c -0.029849246231156
, }. t X! A( K" y5 d8 z -0.029246231155779* K9 t7 o, w+ v- e: H9 c$ }; h5 Q
-0.028643216080402
# T6 d3 C9 L/ X) Q$ i -0.028040201005025( @; ~# P4 @. y" Z2 m4 `* y. X. m
-0.027437185929648
- |3 I2 ~" p1 j# a: L -0.026834170854271: [% Z0 B' X0 M3 R
-0.026231155778894
$ z# Q1 O1 i* Y/ }% p+ q, x. ] -0.025628140703518
% t& E- T' i) |* \1 Y2 b -0.025025125628141( u0 M/ T! s3 u( c5 Q8 U
-0.024422110552764
* u' Z& W) Y4 \) C -0.0238190954773879 U- D1 I8 `6 |* d% @" U4 w4 t0 x
-0.023216080402010
- [' O! S9 p+ z -0.022613065326633
. G1 f0 ~' e. W& d+ B -0.022010050251256# t. @/ Q1 ~) f/ ]) c Z
-0.021407035175879
% _6 M( C% z" E8 C' o6 C6 P+ e -0.020804020100503* G* E. ^ n, j; P
-0.0202010050251262 X; K- N2 }% U3 N& g+ ^- i
-0.0195979899497494 e! U6 T, h4 ~& `- a
-0.018994974874372
* }2 \- w0 G+ H: H -0.018391959798995
5 S% V8 x2 }" b -0.017788944723618+ _& L$ Z# t0 N, }; [
-0.017185929648241
7 w2 R/ W8 B/ |! ^6 c: P0 x! T/ r -0.016582914572864
. G, ?& v, Q+ E& y! o -0.015979899497487$ O5 z7 K/ t8 j3 a' D( X* n. f# h
-0.015376884422111
' Z( Z0 R( `& m* d -0.014773869346734
% R( z; Q/ J' I -0.014170854271357
* U7 M8 L b6 A' k: ?0 m) Y -0.013567839195980& n1 ^+ p n9 w0 ?; T+ s
-0.0129648241206033 O, H- w$ z" M$ R
-0.012361809045226
* B3 t7 K. Y( }) Y -0.0117587939698493 ]8 B& X" d3 j" W
-0.011155778894472$ o' T# N3 Q, Y$ w
-0.010552763819095) t/ w6 H* R8 d: I
-0.009949748743719
8 [3 V( t( _8 ] |" c -0.009346733668342! C3 Q; q% x8 W! K+ `0 h) I
-0.008743718592965
6 K% \6 X, \! w/ i" M' q -0.008140703517588
: M1 d4 x1 A. _7 s -0.007537688442211
* `* p0 v7 d' w9 |. E p -0.0069346733668345 ^$ l) a- O! \' {% ?
-0.006331658291457" T5 y: n- Z" T1 W& i p
-0.0057286432160808 ?* H' x) L3 x4 ~
-0.005125628140704
8 W% u' Z1 [7 T, }+ V& N -0.004522613065327
/ o1 q# p: Z9 _" z5 @ -0.003919597989950
* J4 V6 u; P2 o' B) [/ u0 v3 { -0.003316582914573' }- |1 z V8 J
-0.002713567839196
% F6 N) |$ M& } -0.002110552763819
2 ~6 M7 r4 n3 i" Z+ |) m l -0.001507537688442
( [& s- R, C& d+ V: q: [$ L4 x -0.000904522613065- i% v+ r( ^+ D+ C, {" i, ^+ Y6 ]
-0.000301507537688; h" P6 s' a( i1 O
0.000301507537688: t1 g) p0 D! q- m7 b
0.000904522613065# O( y: u# e2 Q2 C* o- q& x+ n
0.001507537688442
, h9 C6 \& `. @# N6 |& x$ O, ^; d 0.002110552763819
4 F2 D! O" d5 B0 B6 L" _ 0.002713567839196( f6 T: u' A, ~
0.003316582914573; G$ [+ l" `, G' H1 `
0.003919597989950
$ I! ?* N- `3 z 0.004522613065327
- n4 @( w! e$ {8 l% z 0.0051256281407041 Q3 P2 s* S' a1 p
0.005728643216080
8 b- I( T, l, {) F" w9 b; e. c 0.006331658291457
3 l* H' j5 _1 ^2 x k 0.0069346733668341 I h2 T' e; K
0.007537688442211
* p6 X4 p7 V5 v" W) u1 {" L 0.008140703517588: c% t4 V: g1 u2 b& c1 r: n( O
0.008743718592965" A9 D" S# S/ P3 W/ s6 U( _
0.009346733668342( N. F& r7 q& l# e2 S' [5 V0 `. @
0.0099497487437191 s; R8 z8 ?% d% o
0.010552763819095- D6 W$ F2 {% K5 x% _" \8 |
0.011155778894472
/ f# p0 Y/ }, y2 f% t2 o4 M8 s 0.011758793969849) Z3 q, y* M9 [+ V3 h
0.0123618090452266 b M! T3 u) r2 H7 Z! X9 |- X& B
0.012964824120603
, g( r" p& p4 A, { 0.013567839195980 i, w) ~$ i# |) D3 p
0.014170854271357* `0 p+ L5 d% \. o
0.0147738693467340 Y$ o0 i, e( z1 M0 t3 N
0.015376884422111 E! b" ^6 c; i
0.015979899497487
3 q7 K+ B: t# u$ ~# B% R& L 0.016582914572864
2 M4 d$ ~0 l M; g1 l# } 0.017185929648241( a, q. }5 X' E% f0 ~ u6 Z
0.017788944723618/ k7 ~3 Z1 v9 X5 A* F% \
0.018391959798995
6 p- \9 N6 j% v3 |6 i 0.018994974874372
6 e4 C6 w8 j8 t; o7 ?" q 0.019597989949749
, ~- e' x* \6 K. q% J6 s: l" d5 n 0.020201005025126
$ e G, F- c3 e. p- v$ Q9 ` 0.020804020100503
" W! I8 K9 m6 m: Z6 N6 S 0.021407035175879. c3 c8 ?; j7 w' u/ r( M
0.022010050251256+ t" M" t( T- M1 N) N
0.022613065326633' d1 v9 V) \' t
0.023216080402010
8 m8 G1 D4 v u, G+ Q% g+ j 0.023819095477387: S" I1 p- n1 b @+ ]' Q0 |9 @
0.024422110552764) q, `0 z( Y/ ]! W4 g# m4 u
0.025025125628141
- y5 a6 K+ {8 N! f 0.025628140703518
7 ~+ U. B5 \5 X1 O. B% f, v 0.026231155778894
4 O- ^6 ?. ~" }9 b' t# @! T 0.026834170854271" W8 w* }" S2 A+ w
0.027437185929648
7 w2 g7 t% l2 e( V/ G0 V 0.028040201005025
" M- @! Q& @ v0 A" h) f 0.0286432160804025 o1 T$ i/ a% F7 {! [- ], T% l V
0.029246231155779 ]/ G$ D4 S) C4 r0 g8 g
0.029849246231156
# s6 Y1 V. A7 e8 z8 Y8 p 0.030452261306533$ N' B2 o2 P* m
0.031055276381910; ]# w- T4 d, Z& G0 x/ t
0.031658291457286" g$ N7 X6 U, b7 E/ l1 b
0.032261306532663
6 X. `+ s( E; o+ [1 ` 0.032864321608040
6 P* o' R6 x0 ^+ b$ l$ L7 \ 0.033467336683417
7 R8 M. T& ?' `+ { 0.034070351758794
. k7 N/ m* p' h1 F. A 0.034673366834171
# _) W0 P, u$ ?2 x: s 0.0352763819095482 p* g6 e S; Q2 L$ U) y
0.035879396984925
1 ^2 d# z) j8 W( g. S: B 0.036482412060302* _' e- { q# ~; a3 ~3 O) k
0.0370854271356783 O1 e6 o) b1 S$ j; W) b3 O$ k
0.037688442211055
5 ~0 R: [; f. g4 Q 0.038291457286432
+ {. N# I7 f/ ?: u- ^# M( h 0.038894472361809
% X& a% k' {+ _4 E$ [8 w' n. y) d 0.039497487437186
5 ~& S; \8 D- u% F' s' L1 R 0.0401005025125639 w1 }/ ?8 e+ z3 ]' p9 L" J
0.040703517587940+ `% V2 D# n1 ?( ]- }9 p: [! i, x
0.041306532663317
0 b* O, D" E @% K; m1 n, s 0.041909547738693
5 ~2 a n, i- Z, @ t 0.042512562814070
& c+ X( n* K4 A& S4 P0 b 0.043115577889447
. @( M$ f6 Z0 n* z; V 0.043718592964824
2 p! V. V9 L/ @1 }! b8 D# ] 0.044321608040201
5 [: w, L" K% X8 T9 X' e- q 0.044924623115578
4 k, s+ B8 n g9 A% }* W 0.045527638190955
w V' s) c' a 0.046130653266332
w1 _& [# r! N' j, Y6 t 0.046733668341709% K3 T# [1 C; X7 O- P. ~; t
0.047336683417085
- v$ k0 P5 M4 o1 D' ?# }$ f1 S) P" k 0.047939698492462# k0 q/ n# g( I7 E' t
0.048542713567839
6 Q" V4 \% C% u, v 0.049145728643216
# U1 K/ A' z+ N0 L9 Q 0.0497487437185939 W+ T% ?! T1 G6 B. o5 l
0.050351758793970, ^! G. D( X, h* p! M0 c7 ~# T
0.050954773869347
! t& r% S8 k) c 0.051557788944724( ] q9 r6 I u- U7 h# ~: W
0.052160804020101! i8 y' @) U ~( s& i# x
0.0527638190954772 U& S2 m) p% E' ?
0.053366834170854/ M" E+ T" Y# z- D! O
0.053969849246231/ N) a4 q8 V+ f2 q+ f5 u8 P$ h
0.054572864321608
! _: O: p, L3 z0 E2 X8 P 0.055175879396985" `4 w* n1 N1 d( ~$ |
0.0557788944723624 t2 o" A0 D* R0 p. i; u
0.056381909547739
: }1 F& H7 O' k6 v4 v 0.0569849246231163 U$ ?5 M; A! t* V+ \( J; W" Y
0.057587939698492
+ G3 E% L% l+ g% H1 A 0.058190954773869
! R3 o# j ^% x: b( ~. Q) `; U 0.058793969849246
1 e# g6 q/ j n 0.059396984924623$ H2 _. U7 T. U+ ]3 V! x0 N
0.0600000000000001 O. S# e9 _6 F) c! \( ~% G- I
o, e! f4 g4 k2 q- B" l
+ j) K7 u; r1 B- k" l
ans =
7 c3 v* x' L1 P" _8 C& T2 O7 r. q8 I
# a n# X/ J9 N' z -1.033689540653716
# Y) U* f* ]9 y8 [9 @! X) s -1.013619827890691
6 e! T7 w5 e9 N -0.994621366531083
V. b. W- a4 p9 G- v5 C6 E -0.976510534039504
) W+ R& M; A2 T5 \# |2 `. } -0.959151639002957) `5 O( k5 n9 G$ l3 t
-0.942440908631668
( H: r1 @" U% N: w7 ]$ z -0.926296779035772
8 r& |$ Z+ q; E/ G- F* e( f -0.910653694311287
% Q" V8 ]" J8 K. f, | -0.8954579767521012 N& ^6 a: g& w1 M% Q& u) `
-0.8806649792649752 H7 N1 }( `/ i4 Z) H1 O
-0.866237063671064
1 f/ g; p0 F N( u2 X -0.852142129100671+ \6 R: R* ?, W( F( s4 W2 y
-0.838352517460560 @+ B7 U" D; r+ ]9 f5 V' {
-0.824844183890339
) C7 n9 r+ X) I4 y9 M -0.811596057546419
$ a4 Y, H2 S$ A3 N& O9 `+ Y$ z -0.798589541746273( m/ O8 |" c1 U% t5 {
-0.785808117918193
& j( ~, p1 e* _6 V& r) Q2 I: P -0.7732370280687391 n/ K; k+ p6 v; [0 |
-0.760863017467603
* E& c2 ?# h* i5 X' _3 ]. h( M -0.748674124097121+ s8 i- }( O @8 r6 B
-0.736659504835453
% E/ ?# k2 C+ m/ a -0.724809290796292
3 x& {* x1 A: ~9 ^: v" Z -0.713114466033284
% { d e6 i E1 X0 b9 r3 D5 e -0.701566765133452
" G3 n# ?% Y& G. c7 X -0.690158586205827+ t" ~* p7 L' a; r
-0.678882916512848
. Y. I) i W; \1 q) ` -0.667733268556930
5 w. I) Z* M0 H5 i/ C -0.656703624869929% u' m9 i4 U- o
-0.645788390090937
C- D! ~0 ^) \ -0.6349823491828922 e0 p$ x' e! N2 K7 V: s
-0.624280630847343
# F0 E- W9 N- [# \' R -0.613678675363112
8 f" W- v' g; P+ l -0.6031722062077233 O$ C- q2 A! }2 Y1 M# Y
-0.592757204927887( D7 n3 \0 `' d8 }: Z
-0.582429888812360
) ~/ o& W0 S. _9 y% W -0.5721866909916123 p/ [' A' t% E% y- x+ Y1 t
-0.562024242646965' E3 E6 N' l& ?+ J! E7 a
-0.551939357060015
; [4 p3 y; c$ W+ i x' \3 t -0.541929015272840
7 R; Y5 U* `: U: O8 W7 C -0.531990353162879( a$ g# }4 [& t2 [# i* r
-0.522120649763841/ E7 n4 q6 Q1 M9 [
-0.512317316687512& ~4 ^; {" [1 q' M/ |
-0.502577888520921+ S5 } V& s6 n9 n8 A: A' L' R; P% ]
-0.4929000140898369 w! `/ q8 J: V& e
-0.4832814484938857 ~& j, `6 u$ x; q/ l7 `
-0.473720045830499' x$ D$ Z) M2 u8 v! g3 I4 G% S3 x
-0.464213752535263
' Z( ?& Z9 d! p& m$ g; n -0.454760601275071
* N7 @) N2 P; N( Q+ n4 s -0.445358705338140
3 g. f2 ?, p2 ~* c& l$ q8 K) x -0.436006253471471! f+ x2 E( {5 H" v
-0.426701505122098
) h4 m& Y* Y6 E: W. z( V8 ? -0.4174427860433972 p. W: c2 Z- _; }6 ~& G: Z
-0.408228484231992
" \! ~/ C. d" J' a+ C -0.399057046164675" G7 Z- F4 I$ l3 x' A4 R0 m; T: w$ W
-0.389926973307911/ G/ Y% n% v( @! E/ _0 ]
-0.380836818875499
0 m! P F4 u$ E. l& @$ t -0.371785184812454. ]9 T/ A0 o, D5 N+ ?( U( ] q
-0.362770718985392
8 ]: J! S1 r- D% [, o6 B3 J. y" C -0.353792112561766
' `& X, `: _+ [8 f7 M -0.344848097561934$ M7 }" F* u; n; y8 a" J& `
-0.335937444569670
% q9 g; g2 e; T1 C4 ]( g S -0.327058960588106& W* b- C+ Z3 h1 g1 ?0 P3 t
-0.318211487029265" p& r' D `" M; z9 {7 L6 \# Y$ p
-0.309393897826506
' |2 n, s7 i& K' G* x* B -0.300605097660121
9 |; y4 q! F1 o, s6 R/ s -0.2918440202872466 L( Q( ^$ x; Z% T9 V6 C, h" |
-0.283109626967980: _- F/ f: h u& W( s
-0.274400904980369 |" r5 ^3 ?( \3 g, u" i- h
-0.265716866217476
- P$ g) H8 j$ Q8 ]5 C -0.257056545860381
( g1 r; F) ?4 J2 ^; q' y -0.248419001121443
5 |6 Q- [+ d, [* ^: J( w, e4 V -0.239803310052597( g2 W6 U2 Y* h/ g7 m! B
-0.2312085704139354 l. n% e& a' G; c. ~
-0.222633898598121# E7 Z* \; Z- A5 i( R% o+ B
-0.214078428606594
( O8 E6 Q/ A9 T9 }3 v' O' Z -0.2055413110737913 h; d! I( P* P/ `
-0.197021712335900) k, t. k0 d; U$ \6 Z( }
-0.1885188135409222 b9 F0 Y0 I" X7 B
-0.180031809797061
$ X Z0 [4 M9 C( |( f4 V& @ -0.171559909356608( Y% c/ D" Q% }3 V; m9 F* m' B& \" n
-0.163102332832782" t3 e! s# a' b
-0.154658312447061" E5 ^, S0 W3 V
-0.146227091304754
9 w! G, ]- z9 ?; q4 P% _$ R7 G -0.137807922696691
3 S" k: Y, F( G; ] -0.1294000694250411 }8 Q/ J! D# S; A
-0.121002803151371
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3 D [ Q* j) }+ F# i7 @) l0 U
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楼主: shouce
