阳光小院暖茶 发表于 2015-5-14 13:10 ![]()
. C" h0 t- e/ A* P不好意思,我看题目看了几遍,还不知道这个方程是咋样的。光括号就让我迷糊了。帮不了你了 [! f+ g+ {9 L0 m v
我用matlab 重新算了下 A1用t替换 B1用q替换 11/6 用替换 50用R2替换 @& t2 O+ ]3 ^) q( Y
>> syms t q a k A R2' [# [/ R7 f+ h1 j4 s, `1 O8 E3 C
>> x=R2*t*sin(t)+a
* o, `7 w2 D# ]) @
! K1 h' v% s, F9 [# n% n7 C) p7 B7 tx =7 {$ d$ c% [8 e3 }& |3 R8 E/ Z1 J8 W( P
# D4 f# p7 ?) i. da + R2*t*sin(t)
5 H7 o3 ?( r' `" X6 l. @0 L( |7 i2 j. i! c# d8 M
>> y=R2*t*cos(t)* N g0 O. c$ T6 C/ `
% P% ~0 W" F% `
y =
7 L* i! w, ?' v( I8 G2 B; w- d5 p; [( j. I* |
R2*t*cos(t)
5 ?5 Q2 e- F* O0 F! G0 d2 c( c4 S) P% @; _
>> x1=-x*cos(k*q)-y*sin(k*q)+A*cos(q), a) w. O( m) \9 S
. g! ]% y8 m" y4 |; X
x1 =
( w, G, x# N U
/ M2 _9 [: f4 |( H2 M9 WA*cos(q) - cos(k*q)*(a + R2*t*sin(t)) - R2*t*sin(k*q)*cos(t)0 l6 g1 u% i" B8 x9 e- a
8 I7 V# P1 j# Z8 t: C! \9 |>> y1=-x*sin(k*q)+y*cos(k*q)+A*sin(q)
O$ @% p/ k* X/ k2 M% S0 @3 w, o4 O: @
y1 =
0 ]# j1 t3 c4 M8 j
* j u3 X; M+ F4 [, e- e$ A/ S4 uA*sin(q) - sin(k*q)*(a + R2*t*sin(t)) + R2*t*cos(k*q)*cos(t); s% l3 f D$ ~
0 y* _$ ^; \7 g% K
>> diff(x1,t)
. v3 W% w r2 T6 U% B+ U0 z
! v! }9 m/ Z8 J2 L ~8 G" Y' @ans =: U# L) a6 U0 [3 u7 |
Y9 J' b+ i: J+ S4 |* U7 |* ~( BR2*t*sin(k*q)*sin(t) - R2*sin(k*q)*cos(t) - cos(k*q)*(R2*sin(t) + R2*t*cos(t))9 V. ^$ p& F/ x& z1 W c6 _# V. {
( [; {8 N' L6 L( M& @2 K' o2 h
>> diff(x1,q), i6 G% A8 q2 E. U
! q3 K1 S. l( `- [3 n) @& C, J; Y$ mans =4 u4 F, p7 V9 Z4 _
0 ^6 g5 Q$ _3 W& N* j- h& ?1 o
k*sin(k*q)*(a + R2*t*sin(t)) - A*sin(q) - R2*k*t*cos(k*q)*cos(t)" N; V' n7 } q* f( L: x9 C1 m* `
6 |4 v C( Y O+ D3 o( i>> diff(y1,t)
# w( \1 S' {; q. B4 `4 z. }8 I
" F; ?$ x& T" g$ W4 oans =
6 u. s" ?/ r4 \7 y% ]- {) ?5 T1 F9 k* b: B1 E
R2*cos(k*q)*cos(t) - sin(k*q)*(R2*sin(t) + R2*t*cos(t)) - R2*t*cos(k*q)*sin(t)
' Z% c# Y ]9 w3 Y5 G( \# K3 q+ l {5 l
>> diff(y1,q)
7 [" [5 p2 ~" Q- \2 L7 h, r# [( h F0 H
ans =
' {& V, s. F1 \7 _' s! e
% y* u6 O1 Y w# bA*cos(q) - k*cos(k*q)*(a + R2*t*sin(t)) - R2*k*t*sin(k*q)*cos(t)
* Q; _8 Z5 Z1 l: E, T N4 F& l+ J3 @/ v3 t% u x
>> f1=sym('(A*cos(q) - k*cos(k*q)*(a + R2*t*sin(t)) - R2*k*t*sin(k*q)*cos(t))*(R2*t*sin(k*q)*sin(t) - R2*sin(k*q)*cos(t) - cos(k*q)*(R2*sin(t) + R2*t*cos(t)))-(k*sin(k*q)*(a + R2*t*sin(t)) - A*sin(q) - R2*k*t*cos(k*q)*cos(t))*(R2*cos(k*q)*cos(t) - sin(k*q)*(R2*sin(t) + R2*t*cos(t)) - R2*t*cos(k*q)*sin(t))')
& M0 B+ c/ z. s/ C+ s8 y) }& _( Z, Y. d. A$ M$ b# q
f1 =9 Z, d( G+ O1 j
F9 h+ a& }4 q
(k*cos(k*q)*(a + R2*t*sin(t)) - A*cos(q) + R2*k*t*sin(k*q)*cos(t))*(cos(k*q)*(R2*sin(t) + R2*t*cos(t)) + R2*sin(k*q)*cos(t) - R2*t*sin(k*q)*sin(t)) - (A*sin(q) - k*sin(k*q)*(a + R2*t*sin(t)) + R2*k*t*cos(k*q)*cos(t))*(sin(k*q)*(R2*sin(t) + R2*t*cos(t)) - R2*cos(k*q)*cos(t) + R2*t*cos(k*q)*sin(t))
$ \/ i L; L. E( t
4 Y; N+ J2 c' V- U2 }>> simplify(f1)
/ V: C; [! j- [/ D+ d9 r# }" F0 H% d) ]/ B7 M9 v
ans =
m A2 J, ~0 Q M+ l% k
& ?* N- Y8 G+ o+ C3 }A*R2*sin(q - t - k*q) + R2^2*k*t + R2*a*k*sin(t) - A*R2*t*cos(q - t - k*q) + R2*a*k*t*cos(t)
4 d" J6 x) B! ?3 G8 c$ |/ V: Q# i
- ~( d" g) T) N: ?4 N# E, p0 @令 A*R2*sin(q - t - k*q) + R2^2*k*t + R2*a*k*sin(t) - A*R2*t*cos(q - t - k*q) + R2*a*k*t*cos(t)=0' B6 e7 [& D4 A
! b7 _" E6 _ ?* q4 F( k
则q的表达式可手算出来
2 v: ?8 |, L! q; a6 r; [$ P! B3 L
! O' t, v: e0 A, `9 I" r
; e }2 w' m6 A& C% s+ f5 W |