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11#
 楼主
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发表于 2015-11-17 22:57:48
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只看该作者
function solve_nonl_single1V/ }7 a/ c8 L u- v W4 L% S
clear all;clc\% f; Q X5 {" h
format long2 b; n- G+ g7 G* V6 _: k" Y8 F
global a% {7 G, y3 K' W( r9 z
a_span=linspace(-0.06,0.06,200);
, v1 V! l$ h& c- V7 _n=length(a_span);
% S( w9 s6 i5 Q7 Lx0=1e-9;/ S* F3 a% ], m4 g
options=optimset('Algorithm','trust-region-dogleg','TolFun',1e-12,'TolX',1e-12);
* @$ O5 O, W6 k k# H' F# r5 Yfor i=1:n3 s3 E4 C; B% }& M4 a Q0 j
a=a_span(i);5 x4 E% ?5 b9 j1 J: l
x(i)=fsolve(@nonl,x0,options);, l# V5 p. T- b. h; v
y(i)=nonl(x(i));
+ ]& `$ P, T& K, N( D# D& @0 Pend1 r9 S S* }6 p l% {! P
a_span', x',y'$ t5 l" ?" _' r" z
function f=nonl(x)
" a- F+ w8 F, t7 O. q1 [global a) x; R( o9 L! f+ A* m2 L) r3 ~
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));/ R: h! o' V: I/ T& s/ r
8 V y1 U6 q. {运行结果 ans =
' t9 {" g7 p) g h! ~; o" ~2 _. K-0.060000000000000$ Y* H5 @& v" D, _
-0.059396984924623( z6 I6 _0 o7 C/ f W- {
-0.058793969849246
/ P W. _* o; m$ z% `- e' D-0.058190954773869
- H+ F) G0 B8 P( `- ]; g3 q- m. R-0.057587939698492
) Z- t) [, Y/ u' m- I5 {-0.056984924623116
6 k1 K4 a9 x6 k2 M5 b v" t-0.056381909547739! S" b( O1 ~/ [& N1 |
-0.055778894472362
5 A; X% C$ c" d! X9 D1 m-0.055175879396985# i z7 |: S' t! I
-0.054572864321608
2 s6 \# N+ Q& d' r/ r9 |-0.0539698492462317 t/ q& u$ F; f/ a
-0.053366834170854* }' E+ Y. U9 ]9 x2 Y, p# ^" |
-0.0527638190954772 r5 H+ y! ~0 r5 l* z n) u
-0.0521608040201005 ?1 ]- f+ A3 }' u+ g1 A1 U
-0.051557788944724
5 ~# G1 b9 [8 w+ H1 r- U-0.050954773869347
% s' M7 t7 K1 R$ {-0.050351758793970# i: T, w3 y9 ~
-0.049748743718593- I- e* s* s4 d6 ~: c, e$ b8 b6 j
-0.049145728643216. W, K- ~' m& S% \* i+ ^! I; x1 w+ l
-0.048542713567839
/ ~1 c4 A _8 z7 s1 |; f-0.047939698492462! Y0 a( c- l' d" A j! F
-0.047336683417085
6 {; v/ e/ W' J-0.046733668341709
5 Z( f# T8 _7 H-0.0461306532663328 y9 B% T9 A6 r; l: a9 _
-0.045527638190955' d0 K9 L% \. }8 l! M7 q
-0.044924623115578- s$ V0 s! l# i$ O8 |5 l% q4 P
-0.044321608040201
: O% w- g" n( @-0.0437185929648243 k7 `. k0 h& _ C! q! w
-0.043115577889447
' r+ O# w/ d* D1 h-0.0425125628140707 D; x) v3 K+ S/ W' W* g) j
-0.041909547738693
& {: {, f) w0 p; q-0.041306532663317
7 u6 y5 A a- M- I6 n# C# {7 Y-0.040703517587940
6 \! T% T) h9 @/ N1 | e-0.040100502512563
3 O$ F% v/ C, V) F-0.039497487437186
4 w% D0 X- e+ v- V-0.038894472361809/ ?6 K+ ]6 x+ A: ]0 ^! n6 M
-0.038291457286432
3 e/ |6 P H" d D0 n9 M5 Y0 U-0.0376884422110550 k/ i, l4 a0 G- {& N( S
-0.037085427135678& y( |* Y6 V: l# W9 ^* @9 x
-0.036482412060302
1 u! G' ~$ G5 S( T8 v-0.035879396984925
o" G2 y' J) B" g3 F-0.0352763819095482 i1 S' _' T" V! H+ p/ j
-0.0346733668341711 P8 u! F6 k7 b) q
-0.034070351758794
1 F1 l3 N1 O S; j; ^* q-0.033467336683417
" B5 ?; w s2 _! `- `) Z-0.0328643216080401 l- v9 p0 P0 Q
-0.032261306532663+ \- G2 ^6 l$ U. m; P* v
-0.031658291457286
h A9 ?. S8 b-0.031055276381910# ~( m4 \$ m. h
-0.030452261306533
+ A9 m, ~6 G/ J+ Q9 p+ Z$ P-0.0298492462311560 H2 j: V3 P. Z) m9 A- f
-0.0292462311557790 B. G8 M, f: G- b' k
-0.0286432160804021 _! C" |7 L6 t' y7 f9 w3 a
-0.028040201005025" a' N( W( I3 I Y4 s* p) _" l* x6 S
-0.027437185929648
4 `2 ~0 T9 Z8 L, z: [" l) M, N3 M$ _-0.026834170854271
7 r- }! j% A9 j3 b0 M-0.026231155778894
7 |/ o" h5 U' ~5 J# {7 D- ^9 L-0.025628140703518
5 H+ d+ r% Z; M/ K1 H-0.025025125628141+ }: R1 r3 P! ?
-0.0244221105527644 Y* {3 t' u0 a4 w2 M
-0.023819095477387
: ?2 n0 ]' }7 t" I4 P. ]5 \( o! O1 C% }-0.023216080402010) S6 U H8 v0 \) B; K: M
-0.022613065326633
`7 r6 P! p/ B% n, o. e& I-0.022010050251256
3 x5 a4 I$ D5 K* ]-0.021407035175879
: N" N! m, M" X% Q) c+ e9 v5 M-0.020804020100503# B/ A5 R$ f+ L! C4 P
-0.020201005025126. Z" K D5 J* j' I% k9 ]
-0.019597989949749. x- {% J) T+ F* E" `1 Z
-0.018994974874372
9 G/ e( r( L" b" p9 f$ v-0.0183919597989955 Q) W6 p- p! V8 D; S
-0.0177889447236186 a9 n+ o6 A5 r y! |: E. O$ J' b
-0.017185929648241' x" M G2 u9 Q2 f
-0.0165829145728641 |" ?4 X. H0 z0 D2 W! S; k1 D* H
-0.015979899497487
, L+ ]% s5 `+ Z [-0.015376884422111
" Q y6 l& Q4 P! |-0.014773869346734; @$ N# O- ^( p' L1 h' m
-0.014170854271357
+ S5 |+ }! G* ^-0.013567839195980
& s- S8 _7 A" z$ ]( M-0.012964824120603$ a6 s& X0 R6 E0 Q
-0.012361809045226
, i7 v3 C8 O) f, g, `-0.011758793969849: B B" i/ ~. B5 f3 a
-0.011155778894472
3 y0 q c. y) n# A$ a/ z* q' @! \-0.0105527638190956 P& Y2 M9 G8 K& V8 `0 E
-0.009949748743719
. v" y8 B( c. ~-0.009346733668342
! _& z7 e7 h* V/ P- C( m; {- f-0.008743718592965. x" m+ d% Z2 E' K8 T
-0.008140703517588
" [: [% U% q d) Y7 q-0.007537688442211# M; V7 G0 p+ U0 W# I, G2 f
-0.006934673366834. i& c/ b! |6 q* x7 a
-0.0063316582914573 O D; {, a8 J# G- X1 f
-0.005728643216080
( v! d: ~ M- }/ n5 h: J! u- } G-0.005125628140704/ }. x7 n8 P/ P k# B' w, v9 D
-0.004522613065327
/ Q: |, ~$ F: `/ B8 ^* n( }) q-0.003919597989950, w5 t. i9 t( A% Q
-0.003316582914573' _) {4 l% o+ V9 u, k) b
-0.002713567839196
7 Z$ y& R ^, h3 t5 V4 p* N+ R9 n-0.002110552763819
3 d" B2 E, Q' c6 _9 b-0.001507537688442
* ^3 g& ]; J, c: J$ t-0.000904522613065
) ]! v7 o: ^" Z$ o1 B* Q# D9 B-0.000301507537688
# e; J- F! E# w0.000301507537688e% I$ w5 d# Z# h/ I
0.000904522613065; X: T/ @) a8 a, k" z" Q
0.001507537688442( C/ B$ a2 q, f' _ T' R- c( K
0.0021105527638194 u" w$ j2 L5 S
0.002713567839196# T+ K# n, b0 b% ^
0.003316582914573% n) h/ J( g% }' V$ P1 S; c
0.003919597989950
$ B& p; N% F7 M9 @4 X: e5 a; o0.004522613065327( C7 ~' j5 ]! h: e( @
0.005125628140704
* W1 ~$ a8 f0 z0.005728643216080* x- G) H5 c6 L9 h; n# I. j
0.006331658291457
+ J1 N5 {0 ~4 x8 _% u0.006934673366834
0 w9 g4 ~& q) R u9 ^' k0.0075376884422116 n! L7 s* q# {
0.008140703517588
- d9 V1 }1 o9 e0.008743718592965
8 ~9 t# ]) H# s# {8 \4 Q. Z0.009346733668342, ]0 ]* Z& o9 f+ ~/ ]1 f
0.009949748743719
: x8 i A* P8 J) M, S+ u7 T+ }0.010552763819095
" `# m4 ]" {. o7 s) e6 z0 [0.011155778894472% W6 h% J) m( I& X
0.011758793969849- Z9 y7 r& Q& X) n7 p
0.012361809045226
$ @" r" B( T8 `, e. y0.0129648241206037 j, a/ C- {& Q% k1 ? t8 h
0.013567839195980% T. P. v v p: Z( J/ d4 l
0.014170854271357' g% p" C& O- H4 d
0.014773869346734! \- u9 v+ d9 W
0.015376884422111& s; ]( c. U& z3 X+ ~
0.015979899497487
- G/ m) a/ x- {1 q$ {4 Q, b0.0165829145728641 Q8 B$ ~' c' O* o1 X' I
0.017185929648241$ d6 e+ b. O- N) f6 ?
0.0177889447236183 v4 _. K- F8 e
0.0183919597989958 R7 d' M: ]9 d9 Z q; \
0.0189949748743720 y) R9 r6 _6 e9 I) l4 g4 v
0.019597989949749& e6 e+ w, d# |9 F C+ c
0.020201005025126
4 Z$ I: l4 |, j7 j2 E3 N7 W# L0.0208040201005034 N8 ^* w, N; J2 Q3 K( T+ H$ ^
0.021407035175879
2 y( ?6 I }2 @$ G0.022010050251256
) U, G8 U# \' b8 ~0.0226130653266333 o% ]" q4 l: S6 o' [5 X1 G
0.023216080402010
1 K- v1 L& s2 R. {0 V" P: G0.0238190954773873 L. P1 b K- z6 C+ |% i
0.024422110552764
7 t2 \# W4 e# R& {8 _0.0250251256281414 U' c6 Z& y, _
0.0256281407035182 |" B' e( r! d# h6 \
0.026231155778894
( G. Z" @* t7 H8 A4 u0.026834170854271
3 ^; U! h( b. E- Q: ]. h z0.027437185929648% M* E5 K2 G/ k7 h. W* O* e' y
0.0280402010050250 Y7 w5 S1 ~: R/ g4 \- h1 |
0.028643216080402b0 V5 R% T$ K. W
0.029246231155779& `- N: [/ D4 k1 {7 d1 ?
0.0298492462311564 {3 Q, O: Q2 T7 ]1 _( J; l6 X
0.030452261306533
9 Z+ ^ N) I" S1 L/ b0.0310552763819101 `% O9 B# F7 c3 c
0.031658291457286
1 {+ S. H3 n& N6 I) `0 s0.032261306532663
: ?& }) a1 J {( G2 I0.032864321608040& z& B& G0 H6 [ z) R& ]7 v0 r
0.033467336683417
4 b2 v* q$ l; }7 t' N4 n0.034070351758794
- u1 t& {; @4 r) l3 z, q" E; p0.0346733668341711 S6 H* w2 L' g* ^
0.035276381909548) G" H, v6 s z z- p
0.035879396984925! S3 _, L/ H1 V& ^' }
0.036482412060302" C7 k" K1 I8 ]% \0 Z
0.037085427135678
- P; R3 z0 ?5 ]* I+ I2 g: Q' W9 P0.037688442211055
, x5 H* P2 _# X' m# Y* S0.038291457286432
" K' n) s: m- a0.038894472361809+ }" Y% l( g5 x" |* l5 h
0.039497487437186
7 ], D. u) H. U; v: K0.040100502512563
" G$ T( M( K$ K+ _0.040703517587940
" k) R7 J, n& Q, |* O& E h+ q0.0413065326633172 w& W0 a9 a5 n/ M1 ?! j! K
0.041909547738693
$ e/ ^ _6 a" B! ~0.0425125628140707 H5 ^1 H# d! p1 G u, D; u5 d
0.0431155778894479 B, k I' x h5 o: V4 G6 O2 u3 l U
0.043718592964824
; O8 R3 {2 j2 F% }5 T1 o0.0443216080402010 G$ n# U5 y( v# H% p
0.044924623115578
- y- N8 ^# [ K. e3 F0.045527638190955
, y! u3 C V4 _0.046130653266332
3 V5 A1 f& h3 W, g' s. D/ L0.0467336683417090 \, K7 `' Z- |2 c5 U' r# S
0.047336683417085
1 n" R9 e! N5 I+ `# ^ v% }0.047939698492462
) k3 T; l! b( W+ E) m0.048542713567839: q* \: b+ ~% U7 q
0.049145728643216
6 `' E) [9 {) d# _5 j1 J) l6 g0.049748743718593
+ b& {7 G" U: l9 q& G0.050351758793970
9 R8 {* p* J5 B4 }0.050954773869347. b# R1 d) M& q* a5 v5 t/ C
0.051557788944724" J s; `+ U4 a' _
0.052160804020101
2 U9 I o/ O+ E0.052763819095477& V( a& c( n1 t' C
0.053366834170854
J% p ]* z, k! ` |: g. ]/ j0.0539698492462319 j2 Z6 b4 m- ~, m3 m/ `
0.054572864321608
5 y, e# a- \1 y& u# t0.055175879396985- u, M5 F8 N) b$ C3 {
0.055778894472362
( F1 ?: [# Z+ U4 _) N6 J0 h0.0563819095477398 H: y- Q$ h3 H
0.056984924623116* Y2 v' z3 v) }/ K' v3 z0 J
0.057587939698492
9 w9 ?$ [* w5 v' i" M0.058190954773869
9 f' |! c. e, D t8 i0.058793969849246) P9 R, a7 u% V- i T' G& c
0.059396984924623
3 S( N2 R8 D8 q0.060000000000000
0 i2 [: [5 s( t; O4 V, l9 c$ x2 T
+ ?# }% X) r% y4 v- W N
ans =
8 T- I0 ~+ U; I/ d
p2 `" Z2 y0 A/ k-1.033689540653716! D. R* p3 e8 N
-1.013619827890691
1 Y$ x% Y3 w* o) e1 _, I-0.994621366531083, }& M+ g* v& c* W* k+ {
-0.976510534039504! g- l2 V. G% u1 i6 f' @% b
-0.959151639002957) U5 v& x, h- @* h' h- I
-0.942440908631668# ?1 C. O4 f6 p l: N2 Z$ ?! P
-0.9262967790357726 E! `/ {2 D, {9 F3 ]% O
-0.910653694311287
9 F$ e) b: z) M, o-0.895457976752101- ] l; ~ Q% v! Y5 k
-0.8806649792649756 R0 p, U3 s% a1 j' H; H1 y6 Y. @
-0.8662370636710641 b: L, o- S( } c3 p. p
-0.852142129100671# y" b( r( T! n9 A0 X
-0.838352517460560
9 G( y0 T" \. A7 W; ]-0.8248441838903394 A8 N A& l2 _8 S: z) w8 {9 X" V
-0.8115960575464191 d, R& h, w' {0 n' v0 z
-0.798589541746273
& Q% `% X) v1 A1 N-0.785808117918193% `* z; o( X( s+ I9 g9 ^
-0.7732370280687397 }* j; q' c( |" O2 ]7 U9 U
-0.760863017467603
4 c @ N+ S% T q" C) J7 X- c-0.748674124097121" O/ Z% L# J- D! |
-0.7366595048354533 s% c5 x B9 b) v
-0.724809290796292% }" B) J* v9 ^- o
-0.7131144660332847 y, }! ~, _# `. {/ E' \& I& t( n
-0.701566765133452) l. S t7 k$ A2 ~
-0.690158586205827- o) a; l; W; m7 m& y
-0.678882916512848" H5 B7 e) t% \! g
-0.6677332685569302 f1 Y) q( E% N6 \' I4 g
-0.656703624869929
& Z+ j& {8 m* Z-0.6457883900909378 @/ i! o7 F! d$ n+ |8 Q- J
-0.634982349182892) g; z- n6 R* n5 I% v
-0.624280630847343
9 P* \: W) z9 A' N7 A( W" |- T-0.613678675363112
5 @* m! W+ L, w" j9 y4 U-0.603172206207723
B9 H7 c a( l-0.592757204927887
0 |9 Z2 D3 E% Q Q3 V$ E) \-0.582429888812360' | |$ V0 W$ i$ f
-0.572186690991612
: J+ }4 w0 @# T) B5 P-0.562024242646965# g1 \: D# X1 ?2 ?
-0.5519393570600156 C+ \: n9 [6 T, s
-0.541929015272840; }; e1 Z: h1 ^2 \8 V9 P3 l
-0.531990353162879
9 C, B; ?4 J7 M; G* x0 I% Y-0.522120649763841
$ S" x, x' e3 i/ m) a/ M/ J-0.512317316687512
4 K/ d4 {$ w/ ~4 I-0.502577888520921. l& a8 Z" W6 Z
-0.492900014089836
3 `! Z+ J. H {/ v-0.4832814484938852 ]& f& S/ i2 |2 X3 h6 O0 y
-0.473720045830499
z1 x, I: _0 l/ C3 ?2 ?# o; J2 o-0.464213752535263' u2 h7 u* p; J3 c# c( v6 j
-0.454760601275071) D2 t% F3 |; m, ?
-0.445358705338140
% _+ N- x* x5 a8 ^9 Z, t' i# s-0.436006253471471
. W# y6 i5 k+ m" w-0.426701505122098
2 z/ l$ P: h% V! L: t+ i-0.417442786043397
4 R( f+ Y/ }$ z8 w$ i-0.408228484231992- M# c# i, S, @) t% O
-0.399057046164675
' s M- B' ?$ }' V8 E) ?- l& Y-0.389926973307911
5 W, |) T3 g1 [-0.380836818875499# k1 H+ ]5 f) n' |$ l
-0.371785184812454
- L6 g4 ^2 |' u% i* I4 S-0.362770718985392$ g* W5 R" }* X \# _
-0.353792112561766
5 I, L; w$ z; u1 W-0.344848097561934
6 H- @7 x, n4 p/ Z-0.335937444569670/ T; T+ Q6 T% x+ o6 }, e9 s T
-0.327058960588106: S$ q: o4 l% B* w( O
-0.318211487029265% F5 {7 w5 j( X( R! _$ Y2 v; U5 W% z3 o
-0.309393897826506
% @0 P4 W; j) R-0.300605097660121
' |; w( w$ e$ g-0.291844020287246
1 F8 K1 F! L: x3 o, s-0.2831096269679808 e9 `1 K8 g) ?' ^* s: e" Y
-0.2744009049803695 N9 Y9 ?0 T7 A+ [
-0.265716866217476
! T, q8 O, N" G7 e( m) {4 `-0.2570565458603817 m* f& E7 m- F' U- _% A: ^( C: X
-0.248419001121443
6 \/ \; y1 t7 r7 [-0.239803310052597- j; T# r7 {3 R( a3 K. f3 Q' e
-0.231208570413935
8 N8 I) N" W+ [- P$ J-0.222633898598121# G. a: t1 S/ ?% s5 O! R" Y* e
-0.2140784286065944 F3 u2 k, ?, c* @
-0.205541311073791
/ D0 T/ G9 s, f5 U, P-0.1970217123359003 t B; r5 g8 Z
-0.1885188135409222 X# C" u1 I6 P# V' b8 U* I' m* ~
-0.180031809797061. @% I: U1 v; S* x$ m
-0.171559909356608' V' {+ V- Y# u: f% Q. q% Y
-0.163102332832782
6 t. n2 X" i: f, f4 D0 j-0.154658312447061
* V: M) p; T& r3 T U/ ~-0.146227091304754, k: P! \+ A4 m8 R: i- W
-0.1378079226966912 K6 Q7 _5 H, D `6 c1 G
-0.1294000694250413 _9 {% G) `3 _: S; E
-0.1210028031513719 W3 N% [. t9 r
-0.112615403765200
7 s1 m, F# B& V2 B y! E-0.1042371587713628 k0 T9 v i6 S' Q% D
-0.095867362694613
* L: x3 p7 H' V# T& Q% P7 q8 j) l9 Z-0.087505316499959
9 c5 C5 d$ h0 g* {% X. L-0.079150327027304
' u/ [0 ^4 c' a7 P/ u% l+ |! M-0.070801706439035
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