function solve_nonl_single1! F8 ?1 I V, q# t0 g, }% |
clear all;clc2 e4 Y. s/ e3 K( v* R! {
format long
& A+ G; O: W3 q& p' pglobal a" ?& O7 I* g2 W9 W/ S" h" _3 C
a_span=linspace(-0.06,0.06,200);
' [4 J+ J* v3 z* g4 an=length(a_span);
$ F8 {# d% y* A* q Wx0=1e-9; ]- q1 N" k/ {( {! B; W' O
options=optimset('Algorithm','trust-region-dogleg','TolFun',1e-12,'TolX',1e-12);
; g: h0 Q, S/ f- Z- Y" S5 Xfor i=1:n8 Z, p d" L# s) l. V6 L; c
a=a_span(i);) w" D3 I+ O* J1 S% t
x(i)=fsolve(@nonl,x0,options);
9 { m& N0 v5 b' F y(i)=nonl(x(i));8 G1 i' h& o1 ?7 `# {8 N" n% L! H
end, ?: R/ q: a: L( n; f2 h
a_span', x',y'
1 F8 J5 z5 {2 M2 ]3 h8 i. R: j4 M) lfunction f=nonl(x)0 n& @" s$ S& A4 U4 R7 q3 O2 _
global a
$ V) P/ J+ u2 M% c t+ T' lf=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));7 h! O- ]# l+ F( x$ Z% x
( ~2 a" v' b2 x7 h8 M3 |
运行结果 ans =, c2 }( ]5 F |" n7 u
-0.060000000000000: q3 d' _) v3 ?- @: ]) S
-0.0593969849246235 P; I2 @. i# N" s
-0.058793969849246
+ T6 t6 T* W# V: @ -0.058190954773869) b$ P, f8 U! F( ?( w
-0.057587939698492
9 g! s: m h! E5 c" O- n -0.056984924623116
( J1 a+ D: m) m! R+ c* ?& }8 A -0.056381909547739* W* X+ B8 I. h$ b( @2 P- C
-0.0557788944723625 i4 @/ {/ f0 i! h
-0.0551758793969856 J# E/ B1 k' d$ b9 _+ W
-0.054572864321608
( W. @0 J) U& S% T+ n3 [6 q -0.053969849246231
# h* T" ?0 \7 {, C) w# @ -0.0533668341708549 c0 |3 @( C- F5 V& W
-0.052763819095477
$ O# M! o9 w! N* i -0.052160804020100
; D, D, Y: t- y0 w& y( A5 _4 { -0.051557788944724 P) v0 _7 D _/ W, u2 y
-0.050954773869347( I8 u6 d" A, C* ]7 ?
-0.050351758793970
# z" `2 h \" X6 ^1 g -0.049748743718593
- r( }0 j3 R: V# | -0.049145728643216
( h/ ]. C) j2 m$ r -0.048542713567839
, \- j! L7 n! G3 R9 o p -0.047939698492462: r$ m& b& s- H7 g3 z' q; @% T
-0.047336683417085/ D% Y( U) w' S% t
-0.046733668341709
. T* X4 V" W5 W, ` -0.046130653266332
; B0 T2 |, b! G! p- m -0.045527638190955% ]) _" H: n$ u# P8 P5 }4 T
-0.044924623115578
& k" G9 ^5 a9 a8 M -0.044321608040201% |% S! q' U+ r- {% X! q$ u0 V+ R
-0.0437185929648242 W; n! \. L Q8 P7 ~- O6 F. R- M
-0.043115577889447
9 V2 z: t! K6 S/ N5 d6 Z @ -0.042512562814070
9 x- T; J: O' y7 W -0.041909547738693' H) {9 T4 P O5 r6 a* w2 T: }
-0.041306532663317' B3 y6 c' i( |/ X
-0.040703517587940
9 j% \$ ~4 ~6 m, u7 X5 y* V% X -0.040100502512563
1 F" t |/ U" [7 `# G G$ n3 B/ Q -0.0394974874371869 M5 j! G3 M& j+ c" c& g/ T! a
-0.038894472361809
$ L& v3 u& h5 n# V# z& Z -0.038291457286432
# N+ r) Y9 T( y1 z -0.0376884422110555 H) n" U' x( \# n1 }' V9 v3 Q
-0.037085427135678& E) W" }' w$ P" H& o
-0.036482412060302
# f1 b2 R; y) b+ ]( k6 b- d: R -0.0358793969849254 C. \' r; ^6 |& u5 ?
-0.035276381909548
5 }. c& K2 ~* ^4 H. ^3 T -0.034673366834171
* }( e r4 c/ ^+ j) r -0.034070351758794
; w; G* o+ D& P& G& Z3 A+ |- ^ -0.033467336683417
( r% b4 U( o, A4 ~9 @, z9 u -0.0328643216080400 e: \" p9 l$ d) v9 |
-0.032261306532663
7 l7 }6 U+ O1 \3 u. [. L/ c* j5 c -0.031658291457286
& F$ I8 C# R3 j# ^$ g -0.031055276381910
! v3 u+ s% D F) T" Q -0.030452261306533' I7 P$ V4 [+ N! p
-0.029849246231156
1 ?% _- W' h1 q" _ -0.0292462311557791 J: i0 o- O( M D6 X
-0.028643216080402
, H8 C; t4 W% R: J1 f) O0 O+ x -0.028040201005025$ l% Z6 ^$ }1 o, N) J) |# k5 Y
-0.027437185929648
2 p. B6 F. X* f -0.026834170854271; b! Q3 ?6 O- g4 n+ Z: O/ w
-0.026231155778894- N7 l5 O; m5 y( j& f/ K
-0.025628140703518
5 N0 n ^- a4 b& s -0.0250251256281419 G' ^3 D' l, p% L$ Z4 v
-0.024422110552764
) R p3 Y" u5 O% L+ x/ o4 q" V -0.023819095477387
: \ w3 P1 J% O% I. x1 y -0.023216080402010
1 t! J& [# Z7 J! p -0.022613065326633
4 h) S' A, D+ ^ -0.0220100502512562 }$ ^# r4 m3 k/ w
-0.021407035175879" I! F) m G N! q( y% Z- K
-0.020804020100503
* V V, f* d% p: t' Y -0.020201005025126. E7 M0 s" W- _: t W! J
-0.0195979899497495 b) P0 I7 u* h. r/ ^( p: [
-0.018994974874372
1 _2 _ f- e. G6 `9 ] -0.018391959798995
) Y' u6 v2 J5 D! h -0.017788944723618
# y4 a# L( \/ Z: r3 d5 ?4 |, O -0.017185929648241
9 p9 }+ t3 `" N! ~6 T. n% _ -0.0165829145728645 @+ I6 R. m2 s ?: v
-0.015979899497487
& p6 Q: f# \7 {: b; H/ O -0.015376884422111
, m: T$ N8 [. R% w0 r -0.014773869346734
* S7 S: k1 T. c. e) H -0.014170854271357( N4 ?* o$ |0 \( B
-0.013567839195980
5 u1 S! {0 y( H8 A5 g -0.012964824120603$ O3 x5 V* P" V8 Z2 o+ z* P& z1 w
-0.012361809045226
9 l# _" m. }4 }) z4 z -0.011758793969849% x9 l, ?% `- e% y% T8 W: A# q
-0.0111557788944724 ^, I9 C5 Z% p. @& a
-0.010552763819095
( [6 v5 R$ ?0 Q0 v0 j& V" @ -0.009949748743719
, e# i% _1 X( k -0.009346733668342; P0 e3 h" b$ G/ [3 R8 L5 v) P
-0.008743718592965
# R6 P" \' F2 c8 Q( t# d( Q5 \ -0.008140703517588
O! m& q# G& d. _" I+ [8 @( ^* a -0.0075376884422117 C: y3 C% x) I b
-0.006934673366834
# k" I& m' @2 s% `4 j! z/ R) D -0.006331658291457
6 c8 ?/ Z# D; T3 g5 A1 L -0.0057286432160803 Y5 E9 } b( `! Z! m4 l! B; @# x0 d
-0.005125628140704
1 g! J$ M0 N N2 x -0.004522613065327: t- v) U- N$ x, P- p$ N
-0.003919597989950
a% i* X" P9 U) a1 P -0.003316582914573. j; B' Z& j8 I$ ]
-0.0027135678391964 L9 W" B0 b; S7 q6 U% v( O
-0.0021105527638199 P/ }5 m9 n" @* x
-0.001507537688442
: p6 l) {6 H. ~, q2 `) c4 y -0.000904522613065( B; B5 s d; q3 q! j
-0.000301507537688
! @' X0 h( _5 Z& G, m. N/ h 0.000301507537688
$ z+ Y7 q& P2 x N# N" z/ v4 }& B 0.000904522613065
8 o; O) ] N- B& H1 n 0.001507537688442* j7 w _% |! A4 a
0.002110552763819( W( o9 {9 [, K( y, r( Y% N
0.002713567839196& \* D6 w2 G* G# A7 q0 u; n
0.003316582914573
" Y# k9 ^4 o0 C3 b" V2 g: s 0.003919597989950
" i( \1 H. Q- c 0.004522613065327
7 r+ Q2 T8 z, A- T 0.005125628140704
, V+ q; X4 b- M8 x7 P 0.005728643216080
2 H3 c. V% Q/ o R+ f( Y 0.006331658291457
4 H f) A/ H( \4 v' ~& [) W- v 0.006934673366834# f1 @8 n5 R+ e& q. i" ] e
0.007537688442211
6 Y1 h4 G2 g) T' e& a 0.008140703517588
7 k" a2 I, a* {, Y; Z 0.0087437185929656 q2 Q1 Q. C1 W. l, u0 \/ D
0.009346733668342
( [8 |4 b! `% n# C! V 0.009949748743719
4 O4 V9 _' C$ n7 }& _* m7 N' z 0.010552763819095" b# `1 u3 C$ g7 W6 a- N
0.011155778894472; r( ~* y4 P% x
0.011758793969849; X$ g0 M( e6 s
0.012361809045226, r& r$ ~8 f2 N0 n
0.012964824120603
. T F7 m k6 S3 Z+ H: {8 O 0.013567839195980
% u9 f3 Y4 N; u( @+ s2 f s2 Q 0.0141708542713579 @9 b* g" g5 i! o1 Q5 `
0.014773869346734
3 F7 J! Y; f1 k6 Y% a4 Q- \! {4 r2 J 0.0153768844221119 p9 v* W: _- S% Y$ s+ J5 R
0.0159798994974877 q% x! A7 L3 ^6 ~5 A1 D
0.016582914572864
8 G+ K. U- V5 R1 N' g" J 0.017185929648241
3 S }% k# o4 T4 h }$ C) a 0.017788944723618
5 o/ ~$ R+ {9 E K. D* { 0.018391959798995
% B5 Q$ C# g4 l 0.018994974874372* Z) `1 B5 o0 x
0.0195979899497491 H" F: g9 |, g" X
0.020201005025126& T1 q% w* t! a
0.020804020100503/ U0 V! z% D/ s. E
0.021407035175879 q& g) a4 q. Z2 W
0.022010050251256
6 B7 U! _+ R: z' _( ?# Q 0.022613065326633
) b+ y4 k8 h9 j; U; l5 ~ 0.023216080402010" C0 T- N6 C8 K7 K7 t6 j
0.023819095477387% A6 S3 ~7 Z2 I: e, B6 i5 r
0.024422110552764
6 q9 r) l0 V/ B9 K3 G 0.025025125628141
& x* g, ~% E1 P* z) K M 0.025628140703518, U1 f0 v7 H) o
0.026231155778894
4 b8 x. h/ ?" _3 P4 {( M 0.026834170854271* n. J E# h8 {
0.027437185929648
: \! F* [1 L- X( {1 g7 [8 B* P" M 0.028040201005025 n- N, {& h/ C; Y: [6 Q" @% w
0.028643216080402
2 }2 V- }& I% K% k. {5 R 0.029246231155779
8 n; A3 t+ X4 f9 U1 c; S 0.029849246231156/ ~- J l/ t7 m+ [2 {
0.030452261306533
* l/ x; ~$ ~2 H& M( d* E4 ? 0.031055276381910' `" w! F8 Y. f5 _$ G1 M
0.031658291457286 w Y5 \8 }, t( A3 u8 l7 X
0.032261306532663
; ~+ @ r( j8 u8 c( W; Z 0.032864321608040
& x% R. X; @* x" ~" }: q 0.0334673366834177 M0 b# r0 E5 X' c8 O' r5 v
0.034070351758794 F! b" ?% |9 { Y4 H
0.034673366834171; Q/ H* S0 Z- @: t$ n$ B
0.035276381909548
* x9 W! ^6 {4 t3 N: Q 0.035879396984925! t5 |) ~/ r; E' f9 S" m' @& E
0.036482412060302
/ `" v. z! V8 E 0.037085427135678
* A& b- r/ P0 }; k1 Q 0.037688442211055
3 L1 h& t# [# P* K+ @+ z 0.038291457286432+ I2 h. s. Y6 Y5 G/ x1 B/ N
0.038894472361809& P t: R/ g; g( ]- n" {5 W& h3 j
0.0394974874371869 H9 P, G: ^* Y/ [' z3 x" o
0.040100502512563
1 s, F6 z. x& j- J 0.040703517587940; ~1 l) u; b4 d0 V! f# ~
0.0413065326633176 m% U! n0 v* G& [
0.0419095477386938 @+ t5 q; I0 q6 H& }
0.042512562814070' K. C: Q( e p7 s6 H3 _
0.043115577889447- h8 x. @' v. g# i# Z; J
0.043718592964824! v9 {! O' K8 h9 q4 L; s3 B% [
0.0443216080402013 N2 l& ^; c" s/ h, ~, v
0.044924623115578
- V0 U- `( U E/ [+ K 0.045527638190955
, b# _9 r. V4 ~9 \6 J/ k F# o 0.046130653266332
% ~3 y9 k5 w# l7 O' H0 \ 0.046733668341709) x% O( P3 ?5 @9 c3 B
0.047336683417085) |) J/ e) K1 \) S! ^2 Y
0.047939698492462# }1 j. a* c4 g/ E- P
0.048542713567839
9 i- s% I8 Z4 t. }1 p" e 0.049145728643216
; Z$ u9 l- A7 } k1 i- l3 c 0.0497487437185938 E' H1 s* N& Z9 t' y! y0 d" b+ ~& I
0.050351758793970, C$ g4 k/ B/ H2 D
0.050954773869347& a1 n' B2 K2 W& o9 f/ ?
0.051557788944724
5 j. ?; j2 E( I; o# H) B+ u" E 0.052160804020101& b8 O. M# `3 q$ u; m
0.052763819095477: u: d! c4 u `
0.053366834170854/ r% i$ u, O S% ?; A6 ^
0.053969849246231 [5 M4 f' B. \
0.054572864321608) i8 s1 m! [5 E1 I/ \
0.055175879396985
+ n. A. |# }) a" [$ u 0.055778894472362
! z4 Q- K+ K! A7 { 0.056381909547739( Y. X+ u2 v9 e+ m4 ]' ?, Y
0.056984924623116
: n- e8 ]( m1 \& U$ Y& t% N$ ^ 0.057587939698492+ {' \- [9 A. |4 b6 I
0.058190954773869
" Q. f0 Z) \9 a; i 0.0587939698492464 R0 u A9 q- l2 N2 e
0.059396984924623# v3 \5 o5 i# y
0.0600000000000005 n/ i4 [4 j; Z4 ^: S
9 e2 D& v& C' \# ]3 I# q
" ^ s; [" t6 ~; q4 Q8 Gans =
1 O# Y# F8 Q0 M$ L$ |6 [- ?1 l" B% P/ M. ^) l( O
-1.033689540653716
/ [, m1 V- B8 L: @5 J2 T A+ u -1.013619827890691
( V/ t* @) J) |, M# s0 e# Z, V -0.994621366531083
) S0 v3 |" `6 Z. ]- ~: c$ Y -0.9765105340395047 ?! b: _! r8 h4 y) E$ K4 n
-0.959151639002957. I! Z3 ~, E" n% r; s
-0.9424409086316687 r3 V! c- U" k& H
-0.926296779035772 e, y$ L. }# u& O: h
-0.910653694311287$ Z! s7 b, S: X' [& A" g
-0.8954579767521017 o6 h" b& z( \
-0.8806649792649751 P9 d1 M0 B, g# S" a3 {6 N' s$ [2 V
-0.866237063671064
3 ?& e% |+ A- `( F$ `& B2 @ -0.8521421291006719 Z3 P: O+ b# q
-0.838352517460560
6 V7 @6 K" y4 O! t/ o" e5 d -0.8248441838903393 q7 P6 \0 m) ]4 A, N/ T4 h( W
-0.811596057546419( ]3 V+ d: I T3 V5 `3 T( A) e0 z
-0.798589541746273
4 c, L$ J; w$ S -0.785808117918193
4 s2 e, L: @4 ` A! }4 ~ j -0.773237028068739
- X# y% r4 f1 k! { u1 w1 B4 S -0.760863017467603
* D7 w2 Z7 J% ?; V2 d1 T" ? -0.748674124097121; ~7 v0 v: _5 b
-0.736659504835453
5 q7 {8 q8 b4 |9 h5 Z* \ -0.7248092907962923 @7 ]5 D6 F# K+ D
-0.713114466033284
- k# _7 |" {" b! f% _ w -0.701566765133452: J, ^+ b, B3 o3 u( P6 I
-0.690158586205827- s/ d, Y& u. s# e1 V2 ^
-0.678882916512848
0 W }3 e4 o# f8 h3 _0 u -0.667733268556930
; q" T2 }- w! D1 u$ s/ n2 k' M -0.6567036248699292 ? y6 _$ t8 k
-0.645788390090937/ ?; i' ^) _$ [; x- O" ^. p3 Y
-0.634982349182892
& \# e/ y- D+ d7 H/ R -0.624280630847343
- T( @$ a& |/ H1 E! k# J% [ -0.613678675363112
- ~+ E- G. k, r, s9 ? -0.603172206207723
% Q* T; v% K, t. `# }+ } -0.592757204927887
, L5 P8 \6 b1 e$ m# U -0.582429888812360) z l" Z; N! A0 p. x# a- F* m
-0.572186690991612
4 K& a, F1 `5 [- D" h6 S; Z& S: ] -0.562024242646965
2 I9 ] N* m6 O* o1 G5 y -0.551939357060015
& [+ s8 n3 y' J+ b) a -0.5419290152728409 n% y; Y) g+ t" a w* `2 \" z
-0.531990353162879, U3 a. h! |/ ?0 I1 \% p. K
-0.522120649763841- j- |* p' P6 W1 j) L# H& w
-0.512317316687512
! K& e w% ^" [. u7 S; q { -0.502577888520921
0 a+ `' E9 N3 x1 k -0.492900014089836
$ V! f. B/ ? V+ G. M7 X; R -0.483281448493885
& n7 G. Q9 P$ ~% h9 T% s+ E5 x -0.473720045830499
; @3 c9 d9 G+ Y* v/ _+ c$ m -0.464213752535263
- c' f7 z+ {6 u( T9 c1 P+ P -0.454760601275071. K- W% l0 i6 b5 o7 L
-0.4453587053381405 `# h% |- y! H$ i; ?+ M ]+ n% l
-0.4360062534714710 @" c2 f1 S% y5 D1 e
-0.426701505122098( V; I" C3 l1 I& {
-0.417442786043397
% ]8 e' |3 I; ]7 w! | -0.408228484231992, f8 S3 r3 a1 u! H' b
-0.3990570461646753 _6 e5 u* a6 ?, T( b* q& x
-0.389926973307911 R0 { E% n- {( [& ]5 i
-0.380836818875499
) G3 O0 x- @* s& @) t -0.371785184812454
( r. L" e* r+ b+ T/ }5 j -0.362770718985392
$ g1 I! U& U2 g: I; z -0.3537921125617666 Q% h2 \/ ~( L$ ~0 `
-0.344848097561934
8 t( t% X9 T+ U F0 \ -0.3359374445696703 O7 t' r: T3 ?! k W
-0.327058960588106
7 H+ T) n0 k5 d. u5 V8 i -0.3182114870292651 r( _+ f! \2 `+ s
-0.3093938978265066 y- T1 L" w; l* Y5 N4 H
-0.300605097660121! m' W0 {5 R3 i( a/ u) H9 R
-0.291844020287246
) A" ?3 s: }" | -0.283109626967980
6 J9 f1 J1 ] e x -0.2744009049803691 E' r$ i9 @( {
-0.265716866217476
0 `. l \/ O7 H* t, ` -0.257056545860381
! u& p5 s% U3 ~' R( k# ` -0.248419001121443
' C6 b1 p" c. K8 Q3 ~' D4 H -0.2398033100525974 {* g! O# b W. L$ w& z8 V. {
-0.231208570413935
$ l2 s. H* p/ ^0 r7 O( R' |2 T8 N -0.222633898598121
" L( M* t- d* w$ G) v -0.214078428606594
# y- r, x0 j! ?9 t3 t% z -0.205541311073791 K8 p \/ ~$ Q: {+ V
-0.1970217123359006 J* X! c( k2 w: Z V
-0.188518813540922: a1 w/ g m7 H: Y9 r
-0.180031809797061
2 T( D3 R# e9 C+ K -0.1715599093566080 t3 K: D2 n2 ]/ t0 v6 T' B
-0.163102332832782
0 A/ G2 h% I% F& V! S* Q -0.154658312447061
; I1 l# z! G; o+ E: z% F J -0.146227091304754
$ p/ o# X* y! t4 D' z3 X [# B -0.137807922696691
+ t+ g2 K9 Z4 k6 E% D -0.129400069425041- H, O5 M( \! F& N
-0.121002803151371
; `2 R e4 o4 h" }. ^5 Z -0.112615403765200
* j0 `) o9 F: F3 k8 S7 k/ G -0.104237158771362
) P4 _- I1 _% q5 y -0.095867362694613
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楼主: shouce
