godspeedcat
2010-11-06, 14:15
一个三元一次方程组：
m1*x1_dot2 + K12*X1/wn^2 + C12*X1_dot/wn - km1*f*sin(alpha1 + beta1)/wn^2 - cm1*f_dot*sin(alpha1+beta1)/wn...
-m1*e1*theta1_dot^2*cos(theta1 + psi1)/bc - m1*e1*theta1_dot2*sin(theta1 + psi1)/bc = 0;
m1*y1_dot2 + K12*Y1/wn^2 + C12*Y1_dot/wn + km1*f*cos(alpha1+beta1)/wn^2 + cm1*f_dot*cos(alpha1+beta1)/wn...
-m1*e1*theta1_dot^2*sin(theta1+psi1)/bc + m1*e1*theta1_dot2*cos(theta1+psi1)/bc = 0;
(J1 + m1*e1^2)*theta1_dot2 + (kt1*(theta1-thetab1)/wn^2 + ct1*(theta1_dot-thetab1_dot)/wn + kt2*(theta1-thetab2)/wn^2 + ct2*(theta1_dot-thetab2_dot)/wn + km1*f*R1*bc/wn^2 + cm1*f_dot*R1*bc/wn...
-m1*x1_dot2*e1*sin(theta1+psi1)/wn^2 + m1*y1_dot2*e1*cos(theta1+psi1)/wn^2 + T/wn^2) = 0;
目的是解出x1_dot2, y1_dot2, theta1_dot2。
我直接用solve命令解不出来，结果是空解。（不知道为何？请高手解惑，谢谢！）
所以就把方程做了变换，将未知数和其系数整理在方程左边，将非其次项整理在方程右边，并分别用a b c代替。
整理之后的方程如下：
-m1*x1_dot2 + m1*e1*theta1_dot2*sin(theta1 + psi1)/bc =a；
-m1*y1_dot2 - m1*e1*theta1_dot2*cos(theta1+psi1)/bc = b；
m1*x1_dot2*e1*sin(theta1+psi1)/wn^2 - m1*y1_dot2*e1*cos(theta1+psi1)/wn^2 - (J1 + m1*e1^2)*theta1_dot2 = c；
其中：
a = K12*X1/wn^2 + C12*X1_dot/wn - km1*f*sin(alpha1 + beta1)/wn^2 - cm1*f_dot*sin(alpha1+beta1)/wn - m1*e1*theta1_dot^2*cos(theta1 + psi1)/bc)
b = K12*Y1/wn^2 + C12*Y1_dot/wn + km1*f*cos(alpha1+beta1)/wn^2 + cm1*f_dot*cos(alpha1+beta1)/wn - m1*e1*theta1_dot^2*sin(theta1+psi1)/bc);
c = kt1*(theta1-thetab1)/wn^2 + ct1*(theta1_dot-thetab1_dot)/wn + kt2*(theta1-thetab2)/wn^2 + ct2*(theta1_dot-thetab2_dot)/wn + km1*f*R1*bc/wn^2 + cm1*f_dot*R1*bc/wn + T/wn^2);
先用solve解出含有a b c的x1_dot2, y1_dot2, theta1_dot2的表达式，之后将a b c回代到表达式中，求出x1_dot2, y1_dot2, theta1_dot2。
但是，运行之后，x1_dot2, y1_dot2, theta1_dot2的表达式中还是含有a b c。而且，每个x1_dot2, y1_dot2, theta1_dot2 都有两个解！
不知道是何原因，请高手解答，谢谢！
代码如下：
syms m1 x1_dot2 K12 X1 wn C12 X1_dot km1 f alpha1 beta1 cm1 f_dot e1 theta1_dot theta1 psi1 bc theta1_dot2 y1_dot2 Y1 Y1_dot J1 kt1 thetab1 ct1 thetab1_dot kt2 thetab2 ct2 thetab2_dot R1 T a b c
[x1_dot2,y1_dot2,theta1_dot2] = solve('-m1*x1_dot2 + m1*e1*theta1_dot2*sin(theta1 + psi1)/bc =a','-m1*y1_dot2 - m1*e1*theta1_dot2*cos(theta1+psi1)/bc = b','m1*x1_dot2*e1*sin(theta1+psi1)/wn^2 - m1*y1_dot2*e1*cos(theta1+psi1)/wn^2 - (J1 + m1*e1^2)*theta1_dot2 = c');
subs(x1_dot2,a ,K12*X1/wn^2 + C12*X1_dot/wn - km1*f*sin(alpha1 + beta1)/wn^2 - cm1*f_dot*sin(alpha1+beta1)/wn - m1*e1*theta1_dot^2*cos(theta1 + psi1)/bc);
subs(y1_dot2,b, K12*Y1/wn^2 + C12*Y1_dot/wn + km1*f*cos(alpha1+beta1)/wn^2 + cm1*f_dot*cos(alpha1+beta1)/wn - m1*e1*theta1_dot^2*sin(theta1+psi1)/bc);
subs(theta1_dot2,c , kt1*(theta1-thetab1)/wn^2 + ct1*(theta1_dot-thetab1_dot)/wn + kt2*(theta1-thetab2)/wn^2 + ct2*(theta1_dot-thetab2_dot)/wn + km1*f*R1*bc/wn^2 + cm1*f_dot*R1*bc/wn + T/wn^2);
subs(x1_dot2,b, K12*Y1/wn^2 + C12*Y1_dot/wn + km1*f*cos(alpha1+beta1)/wn^2 + cm1*f_dot*cos(alpha1+beta1)/wn - m1*e1*theta1_dot^2*sin(theta1+psi1)/bc);
subs(y1_dot2,c , kt1*(theta1-thetab1)/wn^2 + ct1*(theta1_dot-thetab1_dot)/wn + kt2*(theta1-thetab2)/wn^2 + ct2*(theta1_dot-thetab2_dot)/wn + km1*f*R1*bc/wn^2 + cm1*f_dot*R1*bc/wn + T/wn^2);
subs(theta1_dot2,a ,K12*X1/wn^2 + C12*X1_dot/wn - km1*f*sin(alpha1 + beta1)/wn^2 - cm1*f_dot*sin(alpha1+beta1)/wn - m1*e1*theta1_dot^2*cos(theta1 + psi1)/bc);
subs(x1_dot2,c , kt1*(theta1-thetab1)/wn^2 + ct1*(theta1_dot-thetab1_dot)/wn + kt2*(theta1-thetab2)/wn^2 + ct2*(theta1_dot-thetab2_dot)/wn + km1*f*R1*bc/wn^2 + cm1*f_dot*R1*bc/wn + T/wn^2);
subs(y1_dot2,a ,K12*X1/wn^2 + C12*X1_dot/wn - km1*f*sin(alpha1 + beta1)/wn^2 - cm1*f_dot*sin(alpha1+beta1)/wn - m1*e1*theta1_dot^2*cos(theta1 + psi1)/bc);
subs(theta1_dot2,b, K12*Y1/wn^2 + C12*Y1_dot/wn + km1*f*cos(alpha1+beta1)/wn^2 + cm1*f_dot*cos(alpha1+beta1)/wn - m1*e1*theta1_dot^2*sin(theta1+psi1)/bc);
[x1_dot2,y1_dot2,theta1_dot2]
m1*x1_dot2 + K12*X1/wn^2 + C12*X1_dot/wn - km1*f*sin(alpha1 + beta1)/wn^2 - cm1*f_dot*sin(alpha1+beta1)/wn...
-m1*e1*theta1_dot^2*cos(theta1 + psi1)/bc - m1*e1*theta1_dot2*sin(theta1 + psi1)/bc = 0;
m1*y1_dot2 + K12*Y1/wn^2 + C12*Y1_dot/wn + km1*f*cos(alpha1+beta1)/wn^2 + cm1*f_dot*cos(alpha1+beta1)/wn...
-m1*e1*theta1_dot^2*sin(theta1+psi1)/bc + m1*e1*theta1_dot2*cos(theta1+psi1)/bc = 0;
(J1 + m1*e1^2)*theta1_dot2 + (kt1*(theta1-thetab1)/wn^2 + ct1*(theta1_dot-thetab1_dot)/wn + kt2*(theta1-thetab2)/wn^2 + ct2*(theta1_dot-thetab2_dot)/wn + km1*f*R1*bc/wn^2 + cm1*f_dot*R1*bc/wn...
-m1*x1_dot2*e1*sin(theta1+psi1)/wn^2 + m1*y1_dot2*e1*cos(theta1+psi1)/wn^2 + T/wn^2) = 0;
目的是解出x1_dot2, y1_dot2, theta1_dot2。
我直接用solve命令解不出来，结果是空解。（不知道为何？请高手解惑，谢谢！）
所以就把方程做了变换，将未知数和其系数整理在方程左边，将非其次项整理在方程右边，并分别用a b c代替。
整理之后的方程如下：
-m1*x1_dot2 + m1*e1*theta1_dot2*sin(theta1 + psi1)/bc =a；
-m1*y1_dot2 - m1*e1*theta1_dot2*cos(theta1+psi1)/bc = b；
m1*x1_dot2*e1*sin(theta1+psi1)/wn^2 - m1*y1_dot2*e1*cos(theta1+psi1)/wn^2 - (J1 + m1*e1^2)*theta1_dot2 = c；
其中：
a = K12*X1/wn^2 + C12*X1_dot/wn - km1*f*sin(alpha1 + beta1)/wn^2 - cm1*f_dot*sin(alpha1+beta1)/wn - m1*e1*theta1_dot^2*cos(theta1 + psi1)/bc)
b = K12*Y1/wn^2 + C12*Y1_dot/wn + km1*f*cos(alpha1+beta1)/wn^2 + cm1*f_dot*cos(alpha1+beta1)/wn - m1*e1*theta1_dot^2*sin(theta1+psi1)/bc);
c = kt1*(theta1-thetab1)/wn^2 + ct1*(theta1_dot-thetab1_dot)/wn + kt2*(theta1-thetab2)/wn^2 + ct2*(theta1_dot-thetab2_dot)/wn + km1*f*R1*bc/wn^2 + cm1*f_dot*R1*bc/wn + T/wn^2);
先用solve解出含有a b c的x1_dot2, y1_dot2, theta1_dot2的表达式，之后将a b c回代到表达式中，求出x1_dot2, y1_dot2, theta1_dot2。
但是，运行之后，x1_dot2, y1_dot2, theta1_dot2的表达式中还是含有a b c。而且，每个x1_dot2, y1_dot2, theta1_dot2 都有两个解！
不知道是何原因，请高手解答，谢谢！
代码如下：
syms m1 x1_dot2 K12 X1 wn C12 X1_dot km1 f alpha1 beta1 cm1 f_dot e1 theta1_dot theta1 psi1 bc theta1_dot2 y1_dot2 Y1 Y1_dot J1 kt1 thetab1 ct1 thetab1_dot kt2 thetab2 ct2 thetab2_dot R1 T a b c
[x1_dot2,y1_dot2,theta1_dot2] = solve('-m1*x1_dot2 + m1*e1*theta1_dot2*sin(theta1 + psi1)/bc =a','-m1*y1_dot2 - m1*e1*theta1_dot2*cos(theta1+psi1)/bc = b','m1*x1_dot2*e1*sin(theta1+psi1)/wn^2 - m1*y1_dot2*e1*cos(theta1+psi1)/wn^2 - (J1 + m1*e1^2)*theta1_dot2 = c');
subs(x1_dot2,a ,K12*X1/wn^2 + C12*X1_dot/wn - km1*f*sin(alpha1 + beta1)/wn^2 - cm1*f_dot*sin(alpha1+beta1)/wn - m1*e1*theta1_dot^2*cos(theta1 + psi1)/bc);
subs(y1_dot2,b, K12*Y1/wn^2 + C12*Y1_dot/wn + km1*f*cos(alpha1+beta1)/wn^2 + cm1*f_dot*cos(alpha1+beta1)/wn - m1*e1*theta1_dot^2*sin(theta1+psi1)/bc);
subs(theta1_dot2,c , kt1*(theta1-thetab1)/wn^2 + ct1*(theta1_dot-thetab1_dot)/wn + kt2*(theta1-thetab2)/wn^2 + ct2*(theta1_dot-thetab2_dot)/wn + km1*f*R1*bc/wn^2 + cm1*f_dot*R1*bc/wn + T/wn^2);
subs(x1_dot2,b, K12*Y1/wn^2 + C12*Y1_dot/wn + km1*f*cos(alpha1+beta1)/wn^2 + cm1*f_dot*cos(alpha1+beta1)/wn - m1*e1*theta1_dot^2*sin(theta1+psi1)/bc);
subs(y1_dot2,c , kt1*(theta1-thetab1)/wn^2 + ct1*(theta1_dot-thetab1_dot)/wn + kt2*(theta1-thetab2)/wn^2 + ct2*(theta1_dot-thetab2_dot)/wn + km1*f*R1*bc/wn^2 + cm1*f_dot*R1*bc/wn + T/wn^2);
subs(theta1_dot2,a ,K12*X1/wn^2 + C12*X1_dot/wn - km1*f*sin(alpha1 + beta1)/wn^2 - cm1*f_dot*sin(alpha1+beta1)/wn - m1*e1*theta1_dot^2*cos(theta1 + psi1)/bc);
subs(x1_dot2,c , kt1*(theta1-thetab1)/wn^2 + ct1*(theta1_dot-thetab1_dot)/wn + kt2*(theta1-thetab2)/wn^2 + ct2*(theta1_dot-thetab2_dot)/wn + km1*f*R1*bc/wn^2 + cm1*f_dot*R1*bc/wn + T/wn^2);
subs(y1_dot2,a ,K12*X1/wn^2 + C12*X1_dot/wn - km1*f*sin(alpha1 + beta1)/wn^2 - cm1*f_dot*sin(alpha1+beta1)/wn - m1*e1*theta1_dot^2*cos(theta1 + psi1)/bc);
subs(theta1_dot2,b, K12*Y1/wn^2 + C12*Y1_dot/wn + km1*f*cos(alpha1+beta1)/wn^2 + cm1*f_dot*cos(alpha1+beta1)/wn - m1*e1*theta1_dot^2*sin(theta1+psi1)/bc);
[x1_dot2,y1_dot2,theta1_dot2]