螺桿轉(zhuǎn)子刀具設(shè)計（2） matlab 解法

shouce

螺桿轉(zhuǎn)子刀具設(shè)計 數(shù)學(xué)模型
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- p( L, \4 O, }& d解如下方程：1679999.7*sin(x)-1679997.5*cos(y)*sin(x)-1499997.5*sin(y)*cos(x)-75000*sin(x)^3-179999.4000005*y*cos(y)*cos(x)+179999.4000005*y*sin(y)*sin(x)+75000*cos(y)*cos(x)*sin(x)=0
求當(dāng)x=-1.361時  y=?  
* F/ ~* F+ N' @; }>> syms x y
( Q) L0 u! d6 `) @# M( n3 e>> f=1679999.7*sin(x)-1679997.5*cos(y)*sin(x)-1499997.5*sin(y)*cos(x)-75000*sin(x)^3-179999.4000005*y*cos(y)*cos

(x)+179999.4000005*y*sin(y)*sin(x)+75000*cos(y)*cos(x)*sin(x)

9 j/ X: _& U) E( V  `3 lf =
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(7215543768789811*sin(x))/4294967296 - (2999995*cos(x)*sin(y))/2 - (3359995*cos(y)*sin(x))/2 - 75000*sin(x)^3 + 75000*cos(x)*cos(y)
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) q, ]# u7 X0 R( x8 P9 D*sin(x) - (6184732290414159*y*cos(x)*cos(y))/34359738368 + (6184732290414159*y*sin(x)*sin(y))/34359738368
% Y. Z: G) ]- B) r* k
( H: P7 S- ^- ]>>  subs(f, x, -1.361)
- z4 V3 j! F+ n; ^/ L( c& C
ans =

7 l7 B" ?) D* j5 k$ H4 t$ U7 X(3359995*sin(1361/1000)*cos(y))/2 - (2999995*cos(1361/1000)*sin(y))/2 - (7215543768789811*sin(1361/1000))/4294967296 + 75000*sin

(1361/1000)^3 - 75000*cos(1361/1000)*sin(1361/1000)*cos(y) - (6184732290414159*y*cos(1361/1000)*cos(y))/34359738368 -

(6184732290414159*y*sin(1361/1000)*sin(y))/34359738368
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+ g  j" _/ K$ y* ]5 O4 \9 B# M
/ Y6 d3 @9 U9 e4 x3 Z+ E* @1 k>>  a=0; b=1;
% y; k2 y4 t3 S. V( Feps1=1e-8;eps2=1e-8;
N=300;
( G+ i# c  e2 ~0 T' J4 `f=@ (x) ((3359995*sin(1361/1000)*cos(x))/2 - (2999995*cos(1361/1000)*sin(x))/2 - (7215543768789811*sin(1361/1000))/4294967296 + 75000*sin(1361/1000)^3- 75000*cos(1361/1000)*sin(1361/1000)*cos(x) - (6184732290414159*x*cos(1361/1000)*cos(x))/34359738368 -(6184732290414159*x*sin(1361/1000)*sin(x))/34359738368);
Hfun=@Bisection;
) h+ t: J( X6 B/ {[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);
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; x4 P5 ^* Y( f3 D6 x: n% P2 Z8 P' i3 \運行結(jié)果
k ,a ,b ,x, f
  1, 0.000000000, 1.000000000, 0.500000000,-352805.622314164,
6 y% z) d! H0 a* V& h  2, 0.000000000, 0.500000000, 0.250000000,-92968.331400711,
3 {2 G# G3 R  K( {# X$ `  3, 0.000000000, 0.250000000, 0.125000000,-4146.780462183,
* Y# N2 v" p0 T& A$ X  4, 0.000000000, 0.125000000, 0.062500000,29178.936016433,
- [& P6 f1 ^: q  W5 u" w0 K  5, 0.062500000, 0.125000000, 0.093750000,13458.364371693,
4 S7 ?# k; j4 X6 k/ W% M0 k: h" f6 Q  6, 0.093750000, 0.125000000, 0.109375000,4890.124291139,
: O2 h8 \0 e  E1 S$ n+ m  7, 0.109375000, 0.125000000, 0.117187500,430.092693351,
  8, 0.117187500, 0.125000000, 0.121093750,-1843.759437944,
  9, 0.117187500, 0.121093750, 0.119140625,-703.184646645,
10, 0.117187500, 0.119140625, 0.118164063,-135.633470273,
$ K: J: V0 {9 k: R, d/ W5 K 11, 0.117187500, 0.118164063, 0.117675781,147.457778641,
12, 0.117675781, 0.118164063, 0.117919922,5.969190901,
% q- I/ k/ W; N3 |0 \6 j 13, 0.117919922, 0.118164063, 0.118041992,-64.817881139,
+ \" u! Q8 ~6 A9 T 14, 0.117919922, 0.118041992, 0.117980957,-29.420780403,
; r' H% l3 c/ U& S3 V1 c0 T 15, 0.117919922, 0.117980957, 0.117950439,-11.724903562,
16, 0.117919922, 0.117950439, 0.117935181,-2.877633532,
17, 0.117919922, 0.117935181, 0.117927551,1.545834384,
18, 0.117927551, 0.117935181, 0.117931366,-0.665885649,
19, 0.117927551, 0.117931366, 0.117929459,0.439977849,
' G3 `# q  [) ?. R6 I  \ 20, 0.117929459, 0.117931366, 0.117930412,-0.112953030,
21, 0.117929459, 0.117930412, 0.117929935,0.163512627,
- Y  c0 [* J% [# K& } 22, 0.117929935, 0.117930412, 0.117930174,0.025279853,
  ~4 T5 H# u& [$ m 23, 0.117930174, 0.117930412, 0.117930293,-0.043836575,
+ B6 Q1 h* N; T 24, 0.117930174, 0.117930293, 0.117930233,-0.009278357,
25, 0.117930174, 0.117930233, 0.117930204,0.008000749,
# i! `& V9 s& f3 k 26, 0.117930204, 0.117930233, 0.117930219,-0.000638804,
; I) H. E4 m. N# T2 n: `" z7 | 27, 0.117930204, 0.117930219, 0.117930211,0.003680972,
! V2 t' ~3 }* C9 Q% N( X9 h>>

結(jié)論 當(dāng)x=-1.361時  y=0.117930219
- G1 {  m& \4 K  e' o按此方法   可依次  得出150對x與y的值

單車居士

西交大學(xué)生？？問邢老師

明月山河

你這個是代數(shù)方程？

cosxuan

算法？

shouce

cosxuan 發(fā)表于 2015-6-4 19:45
算法？

# Y3 h, a* S# f) S二分法        
還有一個程序
% Bisection.m
$ D# f! P; \+ F' l6 gfunction[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N)
fprintf('k ,a ,b ,x, f\n')
for k=1:N
: m8 }9 U* O6 ~  ^& ~5 M    x=(a+b)/2;
    f_value=f(x);
    fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...
, W& F$ [! M8 i* I, {1 g      ,k ,a ,b ,x, f_value)
    if abs(f_value)< eps1||0.5*(b-a)<eps2
9 U# `8 A) O! k; R    return
    else
% Y. h5 d  W: @) c, ?9 H! d        if f(x)*f(a)<0
' J9 Y+ @7 g7 D5 n- P          b=x;
% d$ W9 _3 M. c' R( M: A, z% f        else
# m3 i5 l1 c5 a) p( R          a=x;
( O7 u1 Y8 c/ {* O/ e        end
! V! \# j- o: O3 A1 H  \        if k== N
          warning ('算法超出最大迭代數(shù)!')   
/ p% k% f  {) W7 e7 P' R! l        end
- u0 \0 [. C7 t  m; J7 }    end

shouce

單車居士 發(fā)表于 2015-6-4 12:41
2 [8 l4 q1 C" k5 b西交大學(xué)生？？問邢老師

這點問題   自己就可以解決
5 t* H# s5 K* P; l

shouce

明月山河 發(fā)表于 2015-6-4 19:12
你這個是代數(shù)方程？

  c) h2 ^% m  L, W! K0 Q是的呀      不過matlab寫出來的方程  括號很多  不好看   

shouce

明月山河 發(fā)表于 2015-6-4 19:12
* H, N$ I9 A/ ?' Q6 K9 P: J# b4 R你這個是代數(shù)方程？

% Q6 q5 n$ M$ r5 G$ H
" Z* d2 m' P: M% S" Y" g5 f是超越方程      
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& M; Z+ H7 J$ o7 S& h[chāo yuè fāng chéng