螺杆转子刀具设计（2） matlab 解法

shouce

螺杆转子刀具设计 数学模型

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
求当x=-1.361时  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
* I  L# d8 y" K0 m7 d' \& M
(x)+179999.4000005*y*sin(y)*sin(x)+75000*cos(y)*cos(x)*sin(x)
$ J* [% y8 W1 J/ ]' }* O
f =

(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)
& {) s5 M, p) S0 ?6 a5 ?
1 t- j0 `5 @1 k* G% s*sin(x) - (6184732290414159*y*cos(x)*cos(y))/34359738368 + (6184732290414159*y*sin(x)*sin(y))/34359738368
  c# I0 k& S+ ]$ |( `
0 [) A+ M* N2 H>>  subs(f, x, -1.361)
9 g, _# p; f* L2 X( Y
3 d$ e5 y  b4 }* Z# Rans =

(3359995*sin(1361/1000)*cos(y))/2 - (2999995*cos(1361/1000)*sin(y))/2 - (7215543768789811*sin(1361/1000))/4294967296 + 75000*sin

7 E. t- Y) q3 w2 f, S(1361/1000)^3 - 75000*cos(1361/1000)*sin(1361/1000)*cos(y) - (6184732290414159*y*cos(1361/1000)*cos(y))/34359738368 -
+ s% ^/ C+ F8 {7 \; d  r" t
- @+ v( g& a7 Y/ ^(6184732290414159*y*sin(1361/1000)*sin(y))/34359738368

, o5 `) [8 E  V/ x) |9 R
% [2 H7 C6 D8 T# C>>  a=0; b=1;
eps1=1e-8;eps2=1e-8;
1 P9 Q. E( ^2 [( v* }3 n( A2 { N=300;
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;
2 s8 Y/ m! E% T1 M% G6 D- V4 M[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);
. m; d! F4 o+ D0 e0 r/ f
: ~5 V" {/ a5 n运行结果
k ,a ,b ,x, f
  1, 0.000000000, 1.000000000, 0.500000000,-352805.622314164,
- A, h8 N! I4 U4 H3 K' m) ]  _5 j  2, 0.000000000, 0.500000000, 0.250000000,-92968.331400711,
  3, 0.000000000, 0.250000000, 0.125000000,-4146.780462183,
  4, 0.000000000, 0.125000000, 0.062500000,29178.936016433,
  5, 0.062500000, 0.125000000, 0.093750000,13458.364371693,
  6, 0.093750000, 0.125000000, 0.109375000,4890.124291139,
* Y( v# G/ y/ d8 f/ f  _1 u1 @  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,
11, 0.117187500, 0.118164063, 0.117675781,147.457778641,
4 Y1 f3 E8 h, g 12, 0.117675781, 0.118164063, 0.117919922,5.969190901,
* H, ~+ a- V. U 13, 0.117919922, 0.118164063, 0.118041992,-64.817881139,
14, 0.117919922, 0.118041992, 0.117980957,-29.420780403,
6 A' {3 U! r! ` 15, 0.117919922, 0.117980957, 0.117950439,-11.724903562,
! k1 t( @5 P/ v( R$ G- j 16, 0.117919922, 0.117950439, 0.117935181,-2.877633532,
17, 0.117919922, 0.117935181, 0.117927551,1.545834384,
/ E8 c. T' ^& C  L/ p 18, 0.117927551, 0.117935181, 0.117931366,-0.665885649,
19, 0.117927551, 0.117931366, 0.117929459,0.439977849,
3 U; B0 j" I# I; q9 [ 20, 0.117929459, 0.117931366, 0.117930412,-0.112953030,
21, 0.117929459, 0.117930412, 0.117929935,0.163512627,
, `. ?5 R- s* D8 L  ]2 a) } 22, 0.117929935, 0.117930412, 0.117930174,0.025279853,
23, 0.117930174, 0.117930412, 0.117930293,-0.043836575,
24, 0.117930174, 0.117930293, 0.117930233,-0.009278357,
25, 0.117930174, 0.117930233, 0.117930204,0.008000749,
2 r/ j# d% v! b( A/ l- k. ` 26, 0.117930204, 0.117930233, 0.117930219,-0.000638804,
27, 0.117930204, 0.117930219, 0.117930211,0.003680972,
/ M: |4 `! N: G5 F>>

, B( K9 S% \% W7 v结论 当x=-1.361时  y=0.117930219
1 Z+ B! e0 K2 k按此方法   可依次  得出150对x与y的值
* K9 x3 K; f, B* V

shouce

明月山河 发表于 2015-6-4 19:12
) B8 G' ~8 F7 z4 O7 n你这个是代数方程？

9 ]. C* m" o) p' }' y1 b: R" G/ l是超越方程      
4 Z7 S  _8 ?6 p" O/ |; }

1 ]5 c' g2 L/ a. V[chāo yuè fāng chéng

shouce

明月山河 发表于 2015-6-4 19:12
, q: _( B5 z3 k% P& m: M/ U/ `你这个是代数方程？

. z# ^" d: \2 \2 H6 F# q9 ~是的呀      不过matlab写出来的方程  括号很多  不好看   
( P1 D! [0 O, ^* V$ [0 r0 I9 E

shouce

单车居士 发表于 2015-6-4 12:41
0 p$ p$ D4 Y/ A- H西交大学生？？问邢老师

* U. r; B1 [* K/ C5 f7 l8 C: m$ E这点问题   自己就可以解决

shouce

cosxuan 发表于 2015-6-4 19:45
8 |, @8 `% D, d2 H算法？

二分法        
, G$ Q( l  ^- z# \. |; k0 j还有一个程序
% Bisection.m
function[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N)
fprintf('k ,a ,b ,x, f\n')
for k=1:N
! N! G" P; e2 W4 M5 o( g, A# V2 s6 g    x=(a+b)/2;
    f_value=f(x);
    fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...
( `* I. I4 `, f# h6 V1 B      ,k ,a ,b ,x, f_value)
7 j/ o9 F) y; E4 f# D    if abs(f_value)< eps1||0.5*(b-a)<eps2
  C. Q9 i: `3 \% J" F1 m4 u  p    return
    else
& k4 ]9 w) S# }+ o        if f(x)*f(a)<0
          b=x;
( s  O1 \3 Y4 H; `( m* b# }        else
          a=x;
        end
' c- p. I7 X3 o        if k== N
          warning ('算法超出最大迭代数!')   
' R  Q4 _2 u. e        end
+ O( R2 w  ~. H  P8 A  P+ n' T) E7 |    end

cosxuan

算法？

明月山河

你这个是代数方程？

单车居士

西交大学生？？问邢老师