function solve_nonl_single1+ [1 ^: s" j5 e+ ]
clear all;clc( l& r) |5 J- ], ~
format long9 ?$ f$ A/ A0 v% ?5 u
global a g. }2 j0 w* u1 p. H9 |4 m
a_span=linspace(-0.06,0.06,200);
7 J7 T* Z) P l) O. l: a9 Gn=length(a_span);
9 s3 v& U- l1 @6 ]8 B0 zx0=1e-9;) w8 y- E* ~% D. B# U
options=optimset('Algorithm','trust-region-dogleg','TolFun',1e-12,'TolX',1e-12);
7 K# ^! ^+ U. h: ~+ U* m7 D/ ^" Bfor i=1:n& G2 p3 V U# J' S6 u) R
a=a_span(i);
/ ^1 @6 ^+ M' ]. q0 m( P x(i)=fsolve(@nonl,x0,options);' b* Y3 S4 j* S# B( y/ |: E! M
y(i)=nonl(x(i));/ c& H" u* N7 M" W4 H
end" z7 F' k! D; Y4 V" I
a_span', x',y'
/ I8 H5 a7 s6 S6 F" t' @function f=nonl(x)$ S0 q' T1 `) d) i$ x4 n
global a
; V/ [4 e) N% m; _* b/ [% a" V+ E# of=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));
4 l& G! d- h& N& j P* E
1 @( @0 I/ S: g3 b8 ]运行结果 ans =# ?% Y5 C- S1 z! V/ X6 S
-0.0600000000000002 ~6 x* y( N/ h8 p
-0.059396984924623
! {" v& u/ ?7 f' N0 }* \ -0.058793969849246
! o8 O) Z* w: O. t6 c' g -0.058190954773869
3 o$ G$ ^1 h6 }$ F8 ]0 O -0.057587939698492% J+ R! I0 a( g) }8 W, U
-0.056984924623116
. l6 L6 u5 b' h) u1 Y4 p! { Q -0.056381909547739# v+ q" R/ n' X
-0.055778894472362/ a8 G! {" N: X. q4 R
-0.0551758793969859 L7 F% m% |- _/ g
-0.054572864321608
1 @% o; N. {3 Q -0.053969849246231
' d$ y( K& t- o' ~! t- H -0.0533668341708548 Y/ G( ?- N0 X- A) x
-0.052763819095477
3 k* G( V4 L9 G2 q -0.052160804020100. N7 v/ d2 S0 X4 \* A) k
-0.051557788944724
. O8 a6 C8 a; P& `& t1 d5 X1 }# z -0.050954773869347
) k, c6 I5 ^# S2 X) ? -0.050351758793970- B0 w& R9 V6 a* M) b" ]2 s' n
-0.049748743718593) E7 D0 ]2 ?% a" \; c
-0.049145728643216
& [3 K8 f* J A! a! V -0.048542713567839
: _* W. |# \9 s; S" U& P& ` -0.047939698492462: k0 {5 c) D- v5 M( C% ` n; B
-0.047336683417085
5 o" v) g2 o8 \$ N -0.046733668341709- J% c& q& p' Y+ h" f
-0.046130653266332& D( E% V" @' g, b) x4 w5 J
-0.045527638190955: z: X& K% v8 _* n2 N% V3 M# G
-0.044924623115578
4 q& e1 ]* p9 n4 I' y1 H -0.044321608040201+ _3 f* F+ Z: A4 E* R
-0.043718592964824
+ R/ G, M' i9 N+ H- ~7 P -0.043115577889447
9 E" L6 z- d% ~; R% i. O1 j; R -0.042512562814070
6 w. n4 a F- `! F0 X) n) A: o -0.041909547738693' X$ G ]1 x+ `8 M) u% s/ e
-0.041306532663317
5 o* |, X) d6 [* N, r4 L+ { -0.040703517587940
+ l& a% S- Z, J -0.040100502512563
3 C. U. t: J" T -0.0394974874371864 h: }' T; p/ w% K
-0.0388944723618097 V: o$ ]7 E2 d Q2 a2 J1 i, Z9 r
-0.038291457286432( ]0 p1 V5 k- |
-0.037688442211055
2 x! ~# X, u1 O. O4 T$ o -0.037085427135678
; g% h/ ]) @+ x$ H" A! s) e- s+ [ -0.036482412060302, c9 l0 F7 A2 m
-0.035879396984925
9 k% i$ |, c+ l; U6 u3 _( Z -0.035276381909548
5 `, s9 Y) k" o6 l& c -0.034673366834171: o8 A1 Q) O: d4 d
-0.034070351758794
! B0 p8 q( G1 W) b: i -0.033467336683417& V/ H3 P& D* Q( s
-0.032864321608040
9 E( {( Z. Q- c8 H3 {, n -0.032261306532663( T! L4 l# h0 K0 |) ]3 ]
-0.031658291457286" H+ ^1 _! |$ n
-0.031055276381910; F) R' f! H+ Q7 h
-0.0304522613065338 N: f) C2 i& e$ ]9 J' p) v# Y
-0.029849246231156: s( l# w3 |5 e/ C6 z
-0.029246231155779# E Y, N( V y4 w8 ~
-0.028643216080402
3 k. S4 x' ]5 E% s/ c8 T -0.028040201005025
' y0 R2 O. h g; H; F6 ] -0.027437185929648! u7 W: A# @7 t+ M0 v$ F
-0.026834170854271
* x8 F: O! N5 ~' j -0.026231155778894
6 l3 j/ }: k k+ } -0.025628140703518
1 X3 U4 i! `, X- k1 M -0.0250251256281418 p0 ]& t1 M! l: W. Z0 X
-0.024422110552764
( {; u5 o# ?! L. x& W: l2 M H -0.023819095477387
; `0 K0 F9 d2 e9 i -0.023216080402010
: X/ Y9 T7 H) H) _ -0.022613065326633- k. I% h% _" e* L8 j
-0.0220100502512561 u1 f3 v# V3 _* @ P4 \ r* a
-0.021407035175879$ [% |: u2 P" \& n* _
-0.020804020100503
K4 H8 U( \ K+ H: E -0.020201005025126! B P; A* r2 Q% ~
-0.019597989949749
4 W- l6 K* C4 @/ N# m6 I' A -0.0189949748743720 k5 M: Z. ?4 g" g+ l% g/ ~0 q
-0.018391959798995
# d& W) {* k) s" [ -0.0177889447236189 o0 n+ E; B! g, a- b Y2 |
-0.017185929648241! C3 ?- g9 g; {( K# i3 l. q
-0.016582914572864
; H: s+ S9 c1 s. b' G. s -0.015979899497487
- D& R+ F( R$ j" E4 J9 j+ J; P -0.015376884422111. R. @& C) M9 ^% D0 m0 q) ?
-0.014773869346734* n, @/ ^/ @" n0 n
-0.0141708542713572 |* y- G% Q+ T2 A
-0.013567839195980& p# D4 K- s+ z, j( r: q: f2 _
-0.012964824120603
3 G& u4 Q2 W- H5 c -0.0123618090452262 T/ R$ u7 Q7 I& s* t: g) R
-0.011758793969849
& g. ~! t/ w, P! t -0.011155778894472! r: J6 i1 Q6 _1 V! v% D) V" n
-0.0105527638190958 k8 ]3 m B6 ^" w1 a) q$ l
-0.009949748743719* v# w% C# U2 X& q0 x* y
-0.009346733668342
, I% u( `% ]1 K -0.0087437185929655 N% t* ~+ a6 j+ K4 H. a
-0.0081407035175888 V+ i2 A- ]% B2 p
-0.007537688442211
# E- }2 F. V3 V6 s# v! D -0.006934673366834
, _, w. w8 M: h) T$ p) `. c, ]4 F -0.0063316582914572 C0 E; \0 c$ }) N1 x; g" x# w! e
-0.005728643216080# t% x. Y* U* b4 ?& v
-0.005125628140704
6 ]: s3 H0 ]) m, }0 |6 V; e% H6 S6 T -0.0045226130653273 V9 r5 b d8 O' A% R
-0.003919597989950" ^& c, R! K0 u% |% k
-0.003316582914573
" m5 Y( v/ a( @ -0.002713567839196
6 U& P# a6 H5 [, ]0 H -0.002110552763819
5 P5 y& A, L* K5 ] -0.001507537688442% X2 }$ q" h! l+ o
-0.000904522613065
- g* y. M. V) ?* D5 e -0.000301507537688) A/ n' O$ J8 c# V- a, q3 W% }
0.000301507537688, d2 N3 i2 Q+ h, v' y3 J9 T$ {+ q8 R
0.000904522613065; h3 c+ @- G) K% }6 o- }
0.0015075376884423 I9 ?1 R8 z/ P; ~
0.002110552763819
( m' A' I' V8 O, W 0.002713567839196
1 o3 M; i% t$ k* J$ m7 N. U 0.003316582914573! q) b3 I* ]! p4 J3 p d
0.003919597989950
$ R( n* M+ C- [8 [9 Q* q 0.004522613065327
7 M& j( F" v+ }/ \& Y 0.005125628140704
4 b: t+ a; u) ? 0.005728643216080( }& r, r9 j) K0 C" j9 A
0.006331658291457
* G! ^" A$ E0 ?' c 0.006934673366834
2 E" ~* I' M0 y" I 0.007537688442211
/ V+ _8 J( J# u0 G4 Z3 S/ K9 c 0.008140703517588) g0 K- M" X: ^" i$ b/ N
0.008743718592965
/ O5 r6 u) ^ I2 Q7 J 0.0093467336683428 v: F. n; s" ^
0.009949748743719
% `# `8 i+ x: n" C7 M' Z 0.010552763819095
. \/ r' y7 [* I4 h" w 0.011155778894472& y, [ V3 e0 I0 e
0.011758793969849. ], D, u& G! J9 }
0.012361809045226, W4 r. |5 b2 j* }% H0 t& K
0.012964824120603& O7 `3 z9 W$ D
0.013567839195980
; j. j9 ^7 V( v" _0 @' z8 P 0.014170854271357 {- @- E) Q3 @: v5 e' r; t
0.014773869346734" e8 b- M2 O1 `. k# O6 M
0.015376884422111
' A. r6 R$ Y, b3 h# ~# \2 M 0.015979899497487
9 |- \4 ]: q3 F% l% ` 0.016582914572864
9 b6 U0 T0 g( n9 j8 y" k7 ] 0.0171859296482419 e7 u( M1 ^4 V( K' H! R
0.017788944723618
5 y9 p; H* L4 f) `: g, D 0.018391959798995 S6 y" f) p' u% I
0.0189949748743727 h: K" P) m2 [* A
0.019597989949749
# ]" y% v7 d9 g5 \) z9 m( W4 I6 R 0.020201005025126' q8 Z, o% y6 ~6 |7 Z5 s6 a! ^
0.020804020100503" u6 s: Q5 [! e$ U9 j. N2 b1 `; T
0.021407035175879
/ U( Y. @2 n9 m3 d4 W8 X 0.022010050251256: x2 x0 K) N% _- g+ a
0.022613065326633
- [) S- t( |- z7 D: r 0.023216080402010/ \/ {* k& p9 P
0.023819095477387
P$ `2 _6 b" |" ^ P 0.024422110552764! s- h5 T. n# |' M
0.025025125628141
$ x8 [! i" {0 w7 | 0.025628140703518! s3 i) _' y- }! A; Q2 H
0.026231155778894
" z! K. e8 f% @, v; P0 f4 e 0.026834170854271
% t7 z: |) o! R" R 0.027437185929648! s6 Y/ x4 R6 h
0.028040201005025
$ [! F+ A# g% X# H- p 0.0286432160804023 |: Y, I% l- v4 I1 E% h; b0 G
0.029246231155779- a8 ?! l n( h5 c1 s
0.029849246231156
+ G B" A% t% \- o 0.030452261306533
, p6 v2 V% U6 U5 o+ f2 V 0.031055276381910; X$ ?6 }' Y( E3 l6 ?4 ~
0.031658291457286! `( F+ w+ j; n2 w% {4 B6 `# W2 t
0.032261306532663
& Q$ Y( {; N( w/ D& v/ f 0.032864321608040 P& Z/ R( \" w7 [
0.033467336683417* G2 T7 l# [; _/ P) J
0.034070351758794
+ U1 b3 F" S3 ~& k; k 0.0346733668341715 { m* f& P% _/ a
0.035276381909548
( u0 Q0 C9 V6 \0 B6 p2 X7 X- c 0.0358793969849255 @+ h- i$ k; l+ ^; X
0.036482412060302
( D" k) a" M/ o4 D' c( O K$ E 0.037085427135678; H# l$ W" I7 z% {
0.037688442211055
; Q: U7 z# }* C 0.038291457286432
; V) O) u9 j/ I8 v2 S 0.0388944723618099 Q3 v8 A- [$ Y7 z$ ^
0.039497487437186
_4 a6 W7 R0 I- L2 e 0.040100502512563
7 }: W' g! E( \+ x2 l 0.040703517587940* d+ T- M% B6 b6 v
0.041306532663317/ h" z$ z E/ h0 \
0.041909547738693
( \3 o7 t5 L) `+ H 0.042512562814070. e( I3 q3 R7 R& x: f
0.043115577889447
. J6 ?2 M* o" B9 z 0.043718592964824
9 P2 P3 i+ l9 j* _* D7 V: r 0.0443216080402019 c6 z/ |( f! I0 g- R$ e# F
0.044924623115578) c6 B$ W$ T7 }3 i4 c
0.045527638190955
1 k, v5 t4 [5 p* Q- F* Y+ } 0.0461306532663320 m) d4 ^" e, A" S
0.046733668341709
$ O4 E: ]9 \$ @4 P _ 0.047336683417085+ l$ u0 ?& }4 @2 m0 g# q
0.047939698492462$ v4 S- P6 @% [2 w @
0.048542713567839" Y7 U N) F7 `5 s R1 @& b( A
0.049145728643216
, q2 T# w- c7 ]" }" o 0.049748743718593
~5 T' ?2 I* Y9 v$ _ 0.050351758793970
2 Y) \7 H0 l: W* h 0.050954773869347
7 F# p3 T2 Q1 x 0.0515577889447243 {, R& Q; e: i( `+ U
0.052160804020101" Q% [3 ?) T0 g6 d
0.052763819095477, ^1 z6 d8 Y2 b5 G
0.053366834170854; s7 b9 ~; G4 S. r# G! w
0.053969849246231
; y3 X4 \# C% I# K1 x& R, H+ E 0.054572864321608
* D1 C, K9 A3 L) @: v 0.055175879396985
5 M1 q f, C) I& j2 o* H7 K2 ]9 H 0.055778894472362
" S3 K# o% E" d M5 R+ C5 [ 0.056381909547739
5 R2 R0 d) O* m3 M3 ^6 r+ m 0.056984924623116! {4 j, E0 Z9 W5 ~0 J2 y, Y
0.057587939698492
" | ?: f- x! F/ ]2 ?" X9 F6 t 0.058190954773869
- g7 W) u# W: A; u 0.0587939698492461 L2 Z+ D" E# m3 x
0.0593969849246230 b; U! g2 A: j& j0 s/ J
0.060000000000000
& W; U5 y& R8 q( e
+ y+ R7 ]9 e S0 i) j
8 P6 i3 s# e, @ `ans =
* H8 F+ f6 Q& C+ V# b% I7 ?1 O9 ]$ S7 B3 R" h) X, D* Y' z+ R
-1.033689540653716
0 D. s6 u" h) r$ R! ?, W: ~ -1.013619827890691& o& i' y6 u7 D& e
-0.994621366531083( j ?- S6 e6 S% Y
-0.9765105340395043 Q" z# T7 g+ }5 }7 H* Z/ E' K
-0.9591516390029573 d5 T5 h+ @+ I( e- T, U( u
-0.942440908631668
0 l6 Y5 q- j( z' T -0.9262967790357722 C1 f& E( K* q# [0 w
-0.910653694311287" P h1 s4 N6 X/ `" u
-0.8954579767521018 z# y+ s, p+ j( a
-0.880664979264975
3 u5 X8 T; K% b( o$ G -0.866237063671064
) L$ s& [: ]; Z( [ -0.852142129100671
$ o4 v5 B2 ^1 _0 R( V -0.838352517460560
5 O9 P. w& D9 n0 F. O -0.824844183890339
G3 y- A2 n1 H$ q -0.811596057546419% j5 s: i0 J# a& e: D! Q; R
-0.798589541746273
2 A: F( T" F! E' X* B -0.7858081179181939 ~5 k$ i4 ] ]: t5 o. \1 A+ ~
-0.773237028068739
2 ~: G9 Y' y, `0 ^/ q -0.760863017467603
8 W9 S* j0 J4 y% y- b, v -0.748674124097121. a4 J+ |, a( i1 Q4 ]
-0.736659504835453
& V4 x h2 E; c" R -0.724809290796292
& J: k' F+ q, `% f -0.713114466033284% ^1 h- u& ?5 a4 M
-0.7015667651334522 e) S! M& P' B( p$ |' f
-0.690158586205827
# @0 c8 o5 A! I. h/ R& j D& U! ` -0.6788829165128485 p1 J$ u# X$ `
-0.6677332685569305 H( V& m3 f8 U& k$ g
-0.656703624869929
4 J A; \7 }( p- v -0.645788390090937. l' {; T( q6 K. w; Z" ~% K
-0.634982349182892
% F7 m+ ^2 N$ R9 x* N$ K -0.6242806308473437 H$ ^% J" J9 m) s. z
-0.613678675363112
& H" q. L) p. X- r- _1 r -0.603172206207723
4 z6 b8 ~$ s- T I! F8 [ -0.592757204927887
$ G4 E! f; _' p2 F9 n9 ` -0.582429888812360
9 B" ]2 r3 G4 ~$ H( f; ~ -0.572186690991612
. s2 k0 Z4 t/ _$ H6 a \ -0.562024242646965
% I2 `0 @: t' R -0.551939357060015. r1 Y2 L* R8 f$ @0 e
-0.541929015272840
( r- G+ C6 @, o, x' _) { -0.531990353162879
- a- i8 u. T3 d- A -0.5221206497638418 _1 R: f; j7 P& b% h( a {. G. j
-0.512317316687512' J! J2 y( g9 n
-0.502577888520921
4 k/ d+ ^& y# U+ @6 Q" v -0.492900014089836
7 [4 S3 |. S7 j -0.483281448493885
. P, E& w& a# f c" v -0.473720045830499" }1 P2 f3 b4 z2 c c$ {7 g5 p
-0.464213752535263; |3 E; k& k$ U, }8 ~
-0.454760601275071' n5 _( V! p& z
-0.4453587053381408 q" p* A8 q t+ d$ b5 N) D
-0.436006253471471
3 N" Z+ w( Q u) c' L7 L -0.426701505122098
$ @, s$ _4 P0 D3 X7 Q3 c# g( L0 R& b -0.417442786043397- S1 t6 }1 }" F' b+ y+ E; ?
-0.408228484231992. \5 o2 m, y5 N: m$ v
-0.399057046164675- j: Y$ e( x2 |! ?% j! M
-0.389926973307911+ m8 x; s8 H& o% |. U6 I% c
-0.380836818875499
, E8 v% F/ J- r0 I' z2 v -0.371785184812454+ [. c6 c9 Q, y* G& ^5 x
-0.362770718985392
. a8 ?, R2 A# a3 t( l. ] -0.353792112561766
) J" j% z u' A -0.344848097561934; m% _/ a3 S; Z+ H9 R* ~
-0.335937444569670) i/ X$ W& V" j6 \7 p( @! U
-0.3270589605881063 ]- C0 h% Y, b* r: }2 Z M! `
-0.318211487029265
7 M! [6 h! L. {) i% h -0.309393897826506
- e7 f! Z( J" ~- H9 Y -0.300605097660121
: I p. Q( J5 g$ d9 X, I6 V5 } -0.291844020287246
+ ]+ B; ?' w. s6 j: P7 J9 J: x -0.2831096269679805 T* w; p" ]& Y F3 G; y8 ^
-0.274400904980369$ S; p4 p2 `4 B" d3 T" Q
-0.265716866217476" t3 Z8 a) H9 Q% j, i
-0.257056545860381
: E& b# }, C9 Q, [ -0.248419001121443
0 ]3 m/ K1 y: ]( R -0.239803310052597
: k; p0 s/ M+ m0 ~ -0.231208570413935
& o2 R8 o8 H/ [7 H: h0 G -0.222633898598121, X% w6 \2 J' z, q2 F6 ?+ x2 k
-0.2140784286065944 o$ N R ^8 h' R+ K# ^! V
-0.205541311073791; V+ d. h7 G6 s( Q
-0.197021712335900- X i0 c. P1 p }: e
-0.188518813540922" _- \" T" z/ `3 ^7 I- I
-0.180031809797061
6 J2 l! w( z. @1 S2 s -0.171559909356608- t: Y! z7 G$ S
-0.163102332832782' Q# ?) [- F* m4 {& V9 E# b
-0.1546583124470616 R( V2 s/ D Y8 P8 m* s" v: D
-0.146227091304754
$ B6 ]6 r" X4 V& J* Y" z. F2 h# @ -0.137807922696691
( Z" m( W- m0 _4 W; ?6 m/ K" | -0.129400069425041
7 ]$ b" y5 c% h( l -0.121002803151371
$ } Q, B2 i6 w -0.1126154037652005 N: Y! L0 }( k, j
-0.104237158771362 K8 J8 O9 K6 _' ^+ V1 J- K
-0.095867362694613) `9 g! i6 R; K' \ W3 y
-0.087505316499959
( y" y; k. w4 K5 ^5 W -0.079150327027304
/ f, R3 T+ ~6 P/ ?* }! Z -0.0708017064390357 {0 k% S9 e2 R' T% U3 P
-0.062458771679238( F3 j2 t+ K, F, B
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楼主: shouce
楼主