螺桿轉(zhuǎn)子刀具設(shè)計(jì)（2） matlab 解法

shouce

螺桿轉(zhuǎn)子刀具設(shè)計(jì) 數(shù)學(xué)模型

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(shí)  y=?  
>> syms x y
>> 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
! O4 g  }. m2 [- L
; H' `: u. q2 g9 g(x)+179999.4000005*y*sin(y)*sin(x)+75000*cos(y)*cos(x)*sin(x)

: r& A( x. U+ i7 X9 Q  x( }) mf =
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( C6 L! x+ m$ @5 o1 O0 E(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)
; t& w% Z& M2 l  `8 W
*sin(x) - (6184732290414159*y*cos(x)*cos(y))/34359738368 + (6184732290414159*y*sin(x)*sin(y))/34359738368
  l7 d' l  `! K' P
- Y9 [. d% X, `' @; y; x2 t>>  subs(f, x, -1.361)
0 e! f" X1 f/ M
ans =

(3359995*sin(1361/1000)*cos(y))/2 - (2999995*cos(1361/1000)*sin(y))/2 - (7215543768789811*sin(1361/1000))/4294967296 + 75000*sin
# f1 L; W( S1 i/ k
(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
6 E/ u5 [1 w( X
" {9 D; k3 s! L$ W# j( V- E
; t3 O9 T1 v  }>>  a=0; b=1;
0 K4 f+ \7 s$ T+ f/ @9 jeps1=1e-8;eps2=1e-8;
5 j; M7 n" D% r. s: z N=300;
5 x/ [, g2 Z% x8 mf=@ (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;
[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);

運(yùn)行結(jié)果
k ,a ,b ,x, f
3 j" h. n1 l$ }1 y  1, 0.000000000, 1.000000000, 0.500000000,-352805.622314164,
# F8 [1 ?# ^# M' r  2, 0.000000000, 0.500000000, 0.250000000,-92968.331400711,
  3, 0.000000000, 0.250000000, 0.125000000,-4146.780462183,
" V1 G! u) y. L  4, 0.000000000, 0.125000000, 0.062500000,29178.936016433,
  5, 0.062500000, 0.125000000, 0.093750000,13458.364371693,
8 T- y5 L" x! y8 z* F0 U4 M* {  6, 0.093750000, 0.125000000, 0.109375000,4890.124291139,
  n0 l4 `9 u( @) _9 Z4 i8 C$ U  7, 0.109375000, 0.125000000, 0.117187500,430.092693351,
  W: ]8 y1 Z3 ^  @6 ~4 |$ `  8, 0.117187500, 0.125000000, 0.121093750,-1843.759437944,
  9, 0.117187500, 0.121093750, 0.119140625,-703.184646645,
1 W- d" `9 S" M+ [8 a 10, 0.117187500, 0.119140625, 0.118164063,-135.633470273,
: P3 M1 ?' t$ B5 u9 k7 B: M  g3 d 11, 0.117187500, 0.118164063, 0.117675781,147.457778641,
12, 0.117675781, 0.118164063, 0.117919922,5.969190901,
13, 0.117919922, 0.118164063, 0.118041992,-64.817881139,
) W; J6 V& C8 w! c6 Z  z8 M3 G 14, 0.117919922, 0.118041992, 0.117980957,-29.420780403,
4 R6 d* G5 `' i* A5 N3 Y; f8 l 15, 0.117919922, 0.117980957, 0.117950439,-11.724903562,
0 y- }) D; E% D  I. E2 C! j 16, 0.117919922, 0.117950439, 0.117935181,-2.877633532,
! v  m% D9 t2 {9 ~, ? 17, 0.117919922, 0.117935181, 0.117927551,1.545834384,
18, 0.117927551, 0.117935181, 0.117931366,-0.665885649,
, p5 S% F, M, Z" q0 y; ], k 19, 0.117927551, 0.117931366, 0.117929459,0.439977849,
20, 0.117929459, 0.117931366, 0.117930412,-0.112953030,
21, 0.117929459, 0.117930412, 0.117929935,0.163512627,
* w& G% r# z4 s0 o5 M( Y( b/ v 22, 0.117929935, 0.117930412, 0.117930174,0.025279853,
5 h, G. N+ I3 S 23, 0.117930174, 0.117930412, 0.117930293,-0.043836575,
: X8 m  V' C( r7 h% X$ Z 24, 0.117930174, 0.117930293, 0.117930233,-0.009278357,
25, 0.117930174, 0.117930233, 0.117930204,0.008000749,
  R2 x" w0 Y' l( Q" K 26, 0.117930204, 0.117930233, 0.117930219,-0.000638804,
7 n5 j2 g& Z0 \$ B 27, 0.117930204, 0.117930219, 0.117930211,0.003680972,
>>

結(jié)論 當(dāng)x=-1.361時(shí)  y=0.117930219
按此方法   可依次  得出150對(duì)x與y的值

單車居士

西交大學(xué)生？？問(wèn)邢老師

明月山河

你這個(gè)是代數(shù)方程？

cosxuan

算法？

shouce

cosxuan 發(fā)表于 2015-6-4 19:45
, e- W3 _% `, g. {. {! c; K算法？

% P6 e* Q( K9 g2 L二分法        
還有一個(gè)程序
% Bisection.m
function[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N)
8 p' R; [; {( l# f& e4 Ifprintf('k ,a ,b ,x, f\n')
% ^+ W. V1 T" A3 Lfor k=1:N
) ]* D; p5 [4 j3 }8 J    x=(a+b)/2;
7 o7 i8 j, }: D5 u: B7 C    f_value=f(x);
    fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...
      ,k ,a ,b ,x, f_value)
    if abs(f_value)< eps1||0.5*(b-a)<eps2
7 a- ]0 X: D* E0 B. _1 f% w    return
. S7 T0 r# w7 i1 P& V, j/ w) P    else
$ O  e  _& o& @# ~$ X        if f(x)*f(a)<0
          b=x;
        else
          a=x;
/ s. d# q! m! R. F* d9 P        end
& P. I  _: S8 X+ R5 t        if k== N
4 r& Z8 c* V+ R9 T) r, E! e          warning ('算法超出最大迭代數(shù)!')   
+ |, M/ b, j+ m- c: t        end
( v' H. G. X7 L; Q    end

shouce

單車居士 發(fā)表于 2015-6-4 12:41
3 c  Z4 z6 q1 w) g% ?/ H西交大學(xué)生？？問(wèn)邢老師

這點(diǎn)問(wèn)題   自己就可以解決

shouce

明月山河 發(fā)表于 2015-6-4 19:12
6 I5 S0 l* M  V& Z  E6 S" }" z你這個(gè)是代數(shù)方程？

是的呀      不過(guò)matlab寫出來(lái)的方程  括號(hào)很多  不好看   
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6 s' \0 M$ f3 t4 B  n$ w  j

shouce

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

是超越方程      
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[chāo yuè fāng chéng
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