function solve_nonl_single1
& ^# j) O$ |/ b% {* U0 Y2 i/ Aclear all;clc
" z7 j4 e0 V4 F |. lformat long/ y; K$ h# k0 s% ]0 Q1 l+ D
global a
9 |3 L& L: D% W; ~* V# {7 y& sa_span=linspace(-0.06,0.06,200);
. `$ A# T) r3 J% Un=length(a_span);
; w0 ^' y+ y& q8 R) H4 b- P3 jx0=1e-9;1 d: B) ~: ^( a& [7 f
options=optimset('Algorithm','trust-region-dogleg','TolFun',1e-12,'TolX',1e-12);6 ~; Q5 C! Q% |" k% T) D8 E0 T6 f
for i=1:n7 J" n/ e7 i# O3 O0 L3 }# a" B
a=a_span(i);- ~9 }% p7 x* ]* G6 f( |) h
x(i)=fsolve(@nonl,x0,options);% g8 W, G3 k/ \. E5 i: I. b; ?3 ?
y(i)=nonl(x(i));) Z& B3 E9 x5 T3 T
end- { Q3 ^8 c0 a7 Q v
a_span', x',y'" `2 D0 t+ L! R& B7 h% R
function f=nonl(x)
" z. _. F9 d) ]: C R7 ^global a0 A% u/ C8 Z& W3 x
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));2 O5 ~* Z1 S( c" m4 L2 H+ W0 F
/ W9 E* h* x7 \% @, U9 ~$ `运行结果 ans =( O' B( X, d( { x- Z" H ~- n
-0.060000000000000
( A' I8 }- q* y1 Q" @ -0.0593969849246238 H! A) U7 b3 ]4 F
-0.0587939698492464 l( H! [' U* i& B
-0.058190954773869+ I( R) J; V7 b, O0 g; H. @
-0.0575879396984924 _8 W. [1 }( o7 x4 l" {+ H1 _1 g3 Q
-0.056984924623116
, h6 s3 |9 w* Q6 D) Y1 m6 l -0.056381909547739
8 V8 L6 X: h: | p) Q3 [ -0.055778894472362
; T5 V) |! E1 T( G -0.055175879396985( t4 M ]- U9 m7 t* h& l
-0.054572864321608: O3 j8 E; z! U4 y0 @
-0.053969849246231
; o# z$ C' t ^ n! A1 ~8 H+ y -0.0533668341708543 U0 D8 T9 K; R5 X4 G* D& M; b
-0.052763819095477
7 r) M$ h4 Z# ?) u -0.052160804020100% u# b3 _$ Q! ]- @& `( S8 U" ~+ y
-0.051557788944724
3 \" q7 B# z2 r/ A# i5 D% R -0.050954773869347
1 |( n' X& Y' {, a -0.0503517587939708 I2 L+ ]- Z5 Y: x" H. r& z+ m
-0.0497487437185936 r- m: t/ B4 g( L
-0.049145728643216
) W+ Z. J" [, P# t( k# B -0.048542713567839: o- a# [+ q5 W
-0.047939698492462
& j' q0 _ t& L' A! F. e9 h6 X- B -0.047336683417085! A- g/ _0 T9 R
-0.046733668341709
7 ? O) L$ v( H1 @. J0 W6 X5 f+ H$ D6 |8 w -0.046130653266332
% F* F s h. R6 Y8 j( } -0.045527638190955
6 A* z* o, f* C0 c3 v! z -0.0449246231155783 T& `. P; F) U& G
-0.044321608040201+ `% s9 `( J |% G) X, w/ ?, }
-0.043718592964824
' y1 d$ o# b$ q8 p -0.043115577889447
- I5 P8 P3 x7 g, X W: `" U -0.042512562814070
$ n: O2 v4 p& m; g -0.0419095477386933 g& C0 T9 ^8 F) ~- i" N/ l
-0.041306532663317
; l# y0 H( `4 A+ R: z8 i3 h -0.0407035175879407 I# f2 g$ i, d- c
-0.040100502512563
) q& p, m* z0 q( ]: ?7 F -0.039497487437186! f _& e' J! S; ?8 A. B
-0.0388944723618099 t; G0 r/ k, t0 z" U, W; z4 @9 {
-0.038291457286432, _/ {% P! \9 C1 l) |* e) g
-0.037688442211055
8 D, U. Y" F# N" p -0.037085427135678
5 Q/ O, X& _+ }% J* {( o -0.036482412060302! L, o# C" B# `/ r7 a0 ^
-0.035879396984925/ t) D# T4 L* v7 \& W8 u
-0.0352763819095481 _( G" O& t5 E9 U8 f& ~1 }0 A
-0.0346733668341719 o6 b; r7 G$ Q' J6 F
-0.034070351758794
6 Y6 B# ~: }- {$ W8 h2 w! z( n) q -0.0334673366834172 A- l1 I( g* O c1 Z& x
-0.0328643216080404 i/ G. ]/ ^ B# Z# A2 }& \
-0.0322613065326632 r& w8 F- h* U
-0.031658291457286
, ~# a3 v2 s# ^9 k6 G. B3 _ -0.031055276381910! J2 f9 b% i; u/ Y
-0.0304522613065338 G: c/ {7 f9 o
-0.029849246231156 |9 U3 }# w0 Y) L4 `
-0.0292462311557790 h+ C8 V6 T3 t( w
-0.028643216080402& S0 r) |* e" y& a, V3 s
-0.028040201005025
9 u- ^# }7 i9 P: r3 U -0.027437185929648
! A9 ~, D/ z, K- j G% @' o -0.0268341708542719 K3 w8 h9 W- F. s# U. H
-0.026231155778894
W( l2 h- o+ Q6 d -0.025628140703518
6 U) u0 t: Q* f6 b) ] -0.025025125628141
* V4 o- P3 \+ J' M& P0 j -0.024422110552764% ]& n7 J# _9 I2 S
-0.023819095477387
3 {2 g3 f* [3 Z) s0 i -0.023216080402010) P9 {9 V# n' M) G$ T$ l5 d
-0.0226130653266339 _0 C- A4 p: J! o: y, D
-0.0220100502512565 f: \: o& J0 c% I, j; r, {3 Z
-0.021407035175879
/ x: R& x- ]: M8 H9 D4 E1 R -0.020804020100503" w# U ] C6 ` E! P/ n, l) ]* f
-0.020201005025126( b) c+ Z- Q& i0 e2 @7 |
-0.019597989949749
# i/ f2 [7 u2 g6 H -0.018994974874372
# [2 _3 H1 C1 m -0.018391959798995
. S. l5 y2 J: p* ]4 K -0.0177889447236185 T) G4 [; E* o, h: M& m
-0.017185929648241
D! n0 f7 i' x0 b# v. u, k -0.016582914572864
* U! a, ]: d% O6 ?: _ -0.0159798994974876 D/ k) c$ H% f, P3 {! b i
-0.015376884422111
3 o7 C0 _3 q% S" M. u _1 ~ -0.014773869346734) u0 V8 o6 J# L6 O0 d' `, s
-0.014170854271357$ `9 p9 y$ c1 X; A l1 ~
-0.0135678391959806 u/ ?( ]9 T6 s( r: v/ B
-0.0129648241206038 q; k8 A% i% H/ W
-0.012361809045226
6 Q+ l$ {+ s1 I' R7 Z6 O( g9 i& |: Q -0.0117587939698492 g% A D: m8 i. M4 u: ]
-0.011155778894472
; W+ k9 c9 l7 U- k' U -0.010552763819095
* w) y F' K3 J% L6 T) v0 _9 J& X- P& b -0.009949748743719
6 Q! A/ k0 D( K( c0 |6 l* b9 a, s1 X -0.009346733668342& s$ C$ F2 x$ {; w- G
-0.008743718592965# }( n0 v3 G7 N* _0 `/ X, z# U
-0.008140703517588
* V2 ?/ T% E! P* h3 G -0.007537688442211
1 a n3 E" z# r6 U; }$ y' b" n -0.006934673366834* p% `6 A H. V( w$ |
-0.006331658291457
: v0 M: l# d) B( R, e$ O; s -0.005728643216080
, L! ~; V+ L. H3 u+ @/ D -0.005125628140704& B" f* P5 t1 F3 H4 ?* k& T! S
-0.0045226130653272 g2 E2 S: W4 x6 w) w+ q. g
-0.003919597989950
4 ]4 }4 \! q- }6 D, i -0.003316582914573: c1 b' C: p) A* q) {; a: D* t
-0.0027135678391963 `8 J/ i" J7 k; b$ n
-0.002110552763819
+ n0 w% { q I -0.001507537688442
9 w5 H7 q( J% R; H H -0.000904522613065
* c- a6 ^) @' p& ?0 B# Y& Z -0.000301507537688
# F6 W7 r5 m8 }; `% e5 @ 0.000301507537688
B4 C. b, \0 W: S 0.000904522613065* k- F$ ~ m% E1 B7 B; ]6 }9 F
0.001507537688442
/ }9 w4 h# s, g/ s3 O 0.0021105527638190 W/ j* S( }2 W1 r. q' y h
0.002713567839196
7 R- g2 x5 H6 r0 V9 A% L' x 0.0033165829145736 `/ N" g, N3 j! p" n) K: W( ~
0.003919597989950
2 I8 f9 W- S) f 0.004522613065327
+ j/ X4 y" X2 d& C0 h9 ] 0.005125628140704
6 f/ y% ?" q2 e$ ^ 0.005728643216080
$ }" [) H8 M) U: G 0.006331658291457$ j$ G0 H! ^. [4 W
0.0069346733668341 s, r5 K/ _% J# f9 g0 w
0.007537688442211
9 c/ C' ?/ M* @% ]% w) n( ]& W 0.008140703517588
' R J2 {5 G. t! E 0.0087437185929652 A. q' S' {2 N( i
0.0093467336683420 M, M9 d2 ~ {0 W1 w
0.009949748743719( |% _$ A2 e6 Z* t
0.010552763819095: Z6 M5 w: L7 r0 t
0.011155778894472
1 Y, P7 A! i3 _* p! N* C( _1 l! @" X 0.011758793969849
1 @2 ~: u A$ W7 k$ ^" c 0.012361809045226% j9 o4 C: _; M6 K; @/ X% R
0.012964824120603* R! D' o& s( k4 V: a S5 T
0.0135678391959800 K# C3 e7 n- s0 C6 ^) q% d4 B
0.014170854271357
' Q! f; ]5 G# J# o- B D& _% ^ 0.014773869346734
1 j6 Y$ w5 P- b/ W7 G0 ]+ ` 0.015376884422111
/ @7 M% Y" A3 I; y4 \ 0.015979899497487% V' r+ F, I3 E, U& t- s
0.016582914572864
: c7 z( C+ H9 K% s- K, G: d 0.017185929648241
) S9 R N3 K4 l! s6 ` 0.017788944723618
0 G' e t3 C4 U; Q# T 0.018391959798995
3 J- I- b# \; h4 C. o 0.018994974874372' @% J' U0 n4 B4 H6 l+ U# e! Z1 ?
0.019597989949749% f% S* P/ K# l
0.020201005025126! k9 j7 G7 Z+ \% Q# c
0.020804020100503! G9 ^9 {) d# @7 p( }
0.0214070351758790 x# T% H: D8 _" G4 G( u
0.0220100502512567 a4 h2 _* d2 M; u9 ^6 C! f. c
0.022613065326633
) ^; J: p1 a$ P5 L( l5 s0 L6 O$ [ 0.023216080402010
; y; P( j! W% Y" g 0.023819095477387) R' K$ \! w# L6 l
0.0244221105527644 C! X. l I! o% K. C* K
0.025025125628141' q, Z/ J4 Q" [6 d# b( P1 y! K$ X# o6 p
0.0256281407035183 L% @! J! J' K, m% a5 p! x+ }
0.0262311557788948 a; N" k: Z4 j1 P& [
0.026834170854271
- b W5 c+ W; ~ 0.027437185929648( g+ u& U3 ?! P
0.028040201005025
# N' A) }9 U T% ]6 n& M0 s5 v 0.0286432160804022 h: o5 W) ?+ I, {: [, J
0.0292462311557790 ~) p0 g v0 r+ r
0.029849246231156( o% U- s0 V! ~: K4 H
0.030452261306533
" h# E& ~1 B% x- [4 G3 [ 0.031055276381910
; x( A$ U" T( _9 q4 [ 0.031658291457286
/ L. }# e1 c( X4 } 0.032261306532663
- X5 m% q5 C+ r* j# a& \3 w 0.032864321608040
& w" G" w; Y# @! u0 ]$ s' X7 S& d 0.0334673366834174 l! f9 G5 t: P
0.034070351758794
0 k3 q3 a' M$ C; i9 | 0.034673366834171( g/ I( [( b" m5 z/ f9 _" P
0.035276381909548! i$ G# [6 L8 y2 I, L8 e
0.035879396984925
( a' t, X3 O% C0 Z, a& t" \ 0.036482412060302
; E& x8 m h6 M 0.037085427135678
0 J) ] Q/ e% Q0 b 0.0376884422110551 l9 R: h U3 Z0 G1 N' W
0.038291457286432
/ I# N t4 ^0 _$ c$ Z 0.038894472361809
2 D6 V0 x, V) Z5 Z( W' ^ 0.039497487437186
7 s0 [8 q1 T1 [6 A; G: ]" I6 I 0.040100502512563
4 T% K, |, R9 R; N+ N 0.0407035175879408 T7 b: G6 l. N2 e$ h; ]
0.041306532663317* j# N7 a( b9 I @& C3 ^8 Y
0.0419095477386939 ^+ ^& B3 f' Z) p5 |& y) C+ a; J
0.042512562814070/ `* ^( q4 _6 w- ^) X
0.043115577889447
* m2 g0 P( X* ^2 I/ T8 x1 n% H 0.043718592964824
. p+ S/ ~# ]# O4 C7 F& m 0.0443216080402014 b0 p# [5 X" D) U
0.0449246231155788 x, v, C6 @+ A& A: T$ z
0.045527638190955
$ ^0 U9 v A+ N9 i( C' G 0.046130653266332) m7 z+ o: E8 Q4 ?) j4 ~4 w, F* E
0.046733668341709; V, h7 l$ D3 @# @
0.047336683417085, o2 x8 Q1 M& S" n# K: i
0.047939698492462% x$ v$ O; x$ l# p# S2 a
0.0485427135678399 ]6 E" j. B% l# X% I- i4 _
0.049145728643216
# d' j8 b$ E: W5 R 0.049748743718593+ y3 B) V7 `, Y2 P! J
0.050351758793970
4 O1 f; I s. P( k( L$ ~% @ 0.050954773869347
9 i% l* n+ Q; A& [1 {) k/ i 0.051557788944724 g& ^3 x4 f9 c5 ~# o
0.052160804020101! b. w) F! U$ x, {* i
0.052763819095477
. y4 }2 }% R, w0 l/ Y. }4 {8 S 0.0533668341708543 J, X5 |) ~5 H* [, L" j' g8 i
0.053969849246231
4 }: f# o5 E- f. b 0.054572864321608
2 w' Z+ G2 C4 g, k) G4 @ 0.0551758793969853 ?% G4 i# l' E" h8 p
0.055778894472362
0 m# \0 [' u: h/ j/ j- e& T8 l 0.056381909547739
$ k0 v& Z+ c7 M0 ^8 F9 I _" \ 0.0569849246231169 I, ?! l. o- R/ @# P5 w
0.057587939698492
$ ?& i' ? j* z! Z+ @! C/ m" M 0.058190954773869" {. d# y& N8 @, y
0.0587939698492468 o u9 m) |0 W3 _$ a8 }
0.059396984924623
0 ?; o A1 | L8 H 0.060000000000000
9 y! x& |6 _ Q+ o) i! j g- _4 X# W: e# E& N7 K' `
5 C$ {" E$ h" Uans =
& S% y! l2 K+ C3 X+ u2 Z" _ X4 u& o) L7 l/ k/ J3 h
-1.033689540653716
5 ?1 E. c" X0 |6 l r% r -1.013619827890691- m l u9 ?( y4 K: o
-0.994621366531083; x' }9 p. g# A$ ~$ Z9 H
-0.976510534039504" q- ]0 s$ f9 k9 r* U0 L9 G
-0.959151639002957
% ^& N; y0 @3 y A. c- e) A/ a -0.942440908631668
D% B6 g, C( P, d9 m -0.926296779035772
7 c$ R3 H. x6 n% |0 u7 t -0.910653694311287, ?: ?7 B2 W* T& a7 I* {$ U
-0.895457976752101# g5 ~4 m7 d) U% T! U: A- c( J
-0.880664979264975
/ ^* t `2 P7 ]6 S -0.8662370636710644 F+ S( Y( r- U
-0.8521421291006718 Q* ]3 k" T1 D8 m( L" n
-0.838352517460560
/ N0 e4 R% u" U3 W+ ?9 g# ~) Y9 F* ~9 ~, n -0.8248441838903391 ^9 [/ h4 C8 O% y9 j( q
-0.811596057546419
, e" [' T: a3 ^6 I* X5 \, } -0.798589541746273
A- \3 [6 Q9 v -0.7858081179181938 z2 d3 P4 Y+ n$ r
-0.773237028068739! B. `/ u9 D2 T
-0.7608630174676035 m( R; W! I. x3 g I& F
-0.7486741240971216 K. p. Q3 l$ k0 m* w: l
-0.736659504835453
/ l5 M! @, m# Z; J, k: w+ p -0.7248092907962920 P7 M5 c# g4 b
-0.713114466033284
! l2 Q" R% H2 `# w -0.701566765133452' a& a7 V" P! a# ~
-0.690158586205827
: I( o" b6 `# N! w, j! J* V -0.678882916512848' N9 X! r- r9 ^+ r/ @
-0.6677332685569302 J+ V3 g1 |/ l9 j7 s4 ]9 r. p
-0.656703624869929
4 d* w! B3 f) Q8 l1 Z. ]9 p -0.6457883900909375 p0 C" F6 [ t
-0.634982349182892: L$ t/ f! y4 ~3 I, n
-0.624280630847343( N0 M9 p! G6 F* j1 c5 F
-0.613678675363112
( m" S( [- @: P- n* C k -0.6031722062077238 [5 ~2 P1 {/ o( i0 Z+ R; s9 u
-0.592757204927887
3 E! o$ |, D2 M! l -0.582429888812360
8 W/ u! G8 K7 O% x7 a( O -0.572186690991612
" k& E a+ S# Q8 `9 ? -0.562024242646965
6 D/ |! m9 L2 n# ^- \" I -0.5519393570600152 e) L) E. N# ?2 v/ S
-0.541929015272840( K9 d, c5 @/ e2 v% a8 c
-0.531990353162879( D8 U( ?) |3 T5 S( |9 d9 R3 w
-0.5221206497638414 c0 w2 z% l( c
-0.512317316687512; G5 ^5 z* k$ a
-0.502577888520921
3 X5 i: Q0 A4 U -0.492900014089836
3 k2 F7 n2 k$ g+ R/ M) ]% V -0.4832814484938858 L8 `- w6 h1 z+ |/ B8 F
-0.473720045830499
- k: K/ m. ]4 p8 Z# L -0.464213752535263
( a4 S4 W4 d4 l7 s -0.454760601275071
) A: j) r1 w' `+ \* S. s# v$ n; c -0.445358705338140
% a& ~- s% _& a1 _$ x. ]. E -0.436006253471471
$ }; ~( i; g5 d% F2 t% p0 u. @% |! K -0.426701505122098! q. ? ?3 q/ _9 ^
-0.417442786043397
4 d6 q1 J5 R! ?2 o% H3 i V -0.408228484231992
Z0 y) m% s9 }5 p -0.399057046164675
$ s& _* p1 p4 ~" r -0.389926973307911
; ^6 ]! s8 `( i* u w. g -0.3808368188754990 J1 {6 v' l0 \8 l; R& Z
-0.371785184812454
4 C. [6 x/ }' W' S* s -0.362770718985392' `5 t, `; ^6 M0 Q" Y1 G
-0.353792112561766
" c) }2 G3 p: c( q# b -0.344848097561934
, B& C$ \8 ?0 P3 q/ @ -0.3359374445696709 j9 q" } A. R, y0 |1 P
-0.3270589605881069 J: \8 b7 j/ [* f3 B" Z2 O/ C
-0.318211487029265+ \* y* E) F7 T' u" [
-0.309393897826506! i( @( k% j; ~* a8 c1 ]8 K8 u
-0.300605097660121
2 Y5 d. ~5 E$ q+ _ -0.291844020287246, g+ Q- I8 y& l+ G
-0.283109626967980) }- \" y# }5 p! n1 _
-0.274400904980369
* f8 J# V) ]8 P( k( s$ w0 K' C -0.265716866217476
- o6 O6 A6 G* p8 F6 { -0.257056545860381
3 ~/ A2 ^5 F+ ~ }2 f: q% ] -0.248419001121443
% X6 c$ c% m" x" _( r -0.239803310052597 O8 I5 p& L+ I8 L$ B+ R; z
-0.231208570413935
) ?( j# J+ H5 Y8 }; j( }- g -0.222633898598121; ]" D/ _6 ^! s; q
-0.214078428606594! d0 ?) v* l+ O8 A( }% f* T' ?. c3 ^
-0.2055413110737915 b8 c, |! D2 Q
-0.197021712335900/ H& S- }+ F d2 J: g# a
-0.1885188135409225 u+ E# S4 ]% { B
-0.180031809797061
# y! I; z# Q) E1 X -0.171559909356608
7 k! ?9 y+ N/ I$ D; i. }. H -0.163102332832782, s3 j3 n* Y8 d+ v* p& m3 k$ S' N8 k
-0.154658312447061
8 L5 W n3 Q6 `7 e# G5 K -0.146227091304754
7 G* q% s; C2 _2 Q -0.1378079226966917 b0 G! S' X" Z+ K
-0.129400069425041: Z8 ?% ?) Z& T! M0 _
-0.121002803151371
& E c: M' g _* M -0.112615403765200
) N9 d6 [* X/ a -0.104237158771362
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