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[求助]
matlab求解非线性方程组，求助！
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θ1-4未知，用已知表示未知，怎么编程呢？ 这是我编的程序，方程中用l代替l1,m代替l2 >> syms \alpha x y z R r l m \theta_1 \theta_2 \theta_3 \theta_4 eq1=[2^1/2*r*sin(\pi/4-\alpha)*cos\alpha+x-R-l*sin\theta_1]^2+[2^1/2*r*sin(\pi/4-\alpha)*sin\alpha+y]^2+(z+l*cos\theta_1)^2-m^2; eq2=[-2^1/2*r*cos(\pi/4-\alpha)*sin\alpha+x]^2+[2^1/2*r*cos(\pi/4-\alpha)*cos\alpha+y-R-l*sin\theta_2]^2+(z+l*cos\theta_2)^2-m^2; eq3=[-2^1/2*r*sin(\pi/4-\alpha)*cos\alpha+x+R+l*sin\theta_3]^2+[-2^1/2*r*sin(\pi/4-\alpha)*sin\alpha+y]^2+(z+l*cos\theta_3)^2-m^2; eq4=[2^1/2*r*cos(\pi/4-\alpha)*sin\alpha+x]^2+[-2^1/2*r*cos(\pi/4-\alpha)*cos\alpha+y+R+l*sin\theta_4]^2+(z+l*cos\theta_4)^2-m^2; d=solve(eq1,eq2,eq3,eq4) d.\theta_1 \theta_2 \theta_3 \theta_4 ??? Error using ==> syms at 61 Not a valid variable name. 应该怎么改啊？十分感谢！  方程组 |
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2楼2012-05-21 13:29:15
3楼2012-05-21 14:15:38
4楼2012-05-21 14:20:32
5楼2012-05-21 14:28:47
6楼2012-05-21 14:38:22
【答案】应助回帖
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d=solve(eq1,'theta_1') d = 2*atan((2*(2*l*x - 2*R*l + ((4*l*x - 4*R*l + 2*2^(1/2)*l*r - 8*R*l*tan(alpha/2)^2 - 4*R*l*tan(alpha/2)^4 + 8*l*x*tan(alpha/2)^2 + 4*l*x*tan(alpha/2)^4 - 4*2^(1/2)*l*r*tan(alpha/2)^2 + 4*2^(1/2)*l*r*tan(alpha/2)^3 + 2*2^(1/2)*l*r*tan(alpha/2)^4 - 4*2^(1/2)*l*r*tan(alpha/2))^2/4 - ((r^2*cos(alpha)^4)/2 - 2*l*z - 2*R*x + 2*R^2*tan(alpha/2)^2 + R^2*tan(alpha/2)^4 + R^2 + 2*l^2*tan(alpha/2)^2 + l^2*tan(alpha/2)^4 - 2*m^2*tan(alpha/2)^2 - m^2*tan(alpha/2)^4 + l^2 + 2*x^2*tan(alpha/2)^2 + x^2*tan(alpha/2)^4 - m^2 + 2*y^2*tan(alpha/2)^2 + y^2*tan(alpha/2)^4 + 2*z^2*tan(alpha/2)^2 + z^2*tan(alpha/2)^4 + x^2 + y^2 + z^2 - r^2*cos(alpha)^3*sin(alpha) + (r^2*cos(alpha)^2*sin(alpha)^2)/2 + r^2*sin(alpha)^2*sin(alpha - pi/4)^2 - 4*R*x*tan(alpha/2)^2 - 2*R*x*tan(alpha/2)^4 - 4*l*z*tan(alpha/2)^2 - 2*l*z*tan(alpha/2)^4 + r^2*tan(alpha/2)^2*cos(alpha)^4 + (r^2*tan(alpha/2)^4*cos(alpha)^4)/2 - 2*r*y*sin(alpha)*sin(alpha - pi/4) + r^2*tan(alpha/2)^2*cos(alpha)^2*sin(alpha)^2 + (r^2*tan(alpha/2)^4*cos(alpha)^2*sin(alpha)^2)/2 + 2*r^2*tan(alpha/2)^2*sin(alpha)^2*sin(alpha - pi/4)^2 + r^2*tan(alpha/2)^4*sin(alpha)^2*sin(alpha - pi/4)^2 - 2^(1/2)*R*r*cos(alpha)^2 - 2*r^2*tan(alpha/2)^2*cos(alpha)^3*sin(alpha) - r^2*tan(alpha/2)^4*cos(alpha)^3*sin(alpha) + 2^(1/2)*r*x*cos(alpha)^2 + 2^(1/2)*R*r*cos(alpha)*sin(alpha) - 2*2^(1/2)*R*r*tan(alpha/2)^2*cos(alpha)^2 - 2^(1/2)*R*r*tan(alpha/2)^4*cos(alpha)^2 - 2^(1/2)*r*x*cos(alpha)*sin(alpha) + 2*2^(1/2)*r*x*tan(alpha/2)^2*cos(alpha)^2 + 2^(1/2)*r*x*tan(alpha/2)^4*cos(alpha)^2 - 4*r*y*tan(alpha/2)^2*sin(alpha)*sin(alpha - pi/4) - 2*r*y*tan(alpha/2)^4*sin(alpha)*sin(alpha - pi/4) + 2*2^(1/2)*R*r*tan(alpha/2)^2*cos(alpha)*sin(alpha) + 2^(1/2)*R*r*tan(alpha/2)^4*cos(alpha)*sin(alpha) - 2*2^(1/2)*r*x*tan(alpha/2)^2*cos(alpha)*sin(alpha) - 2^(1/2)*r*x*tan(alpha/2)^4*cos(alpha)*sin(alpha))*(2*l*z - 2*R*x + (r^2*cos(alpha)^4)/2 + 2*R^2*tan(alpha/2)^2 + R^2*tan(alpha/2)^4 + R^2 + 2*l^2*tan(alpha/2)^2 + l^2*tan(alpha/2)^4 - 2*m^2*tan(alpha/2)^2 - m^2*tan(alpha/2)^4 + l^2 + 2*x^2*tan(alpha/2)^2 + x^2*tan(alpha/2)^4 - m^2 + 2*y^2*tan(alpha/2)^2 + y^2*tan(alpha/2)^4 + 2*z^2*tan(alpha/2)^2 + z^2*tan(alpha/2)^4 + x^2 + y^2 + z^2 - r^2*cos(alpha)^3*sin(alpha) + (r^2*cos(alpha)^2*sin(alpha)^2)/2 + r^2*sin(alpha)^2*sin(alpha - pi/4)^2 - 4*R*x*tan(alpha/2)^2 - 2*R*x*tan(alpha/2)^4 + 4*l*z*tan(alpha/2)^2 + 2*l*z*tan(alpha/2)^4 + r^2*tan(alpha/2)^2*cos(alpha)^4 + (r^2*tan(alpha/2)^4*cos(alpha)^4)/2 - 2*r*y*sin(alpha)*sin(alpha - pi/4) + r^2*tan(alpha/2)^2*cos(alpha)^2*sin(alpha)^2 + (r^2*tan(alpha/2)^4*cos(alpha)^2*sin(alpha)^2)/2 + 2*r^2*tan(alpha/2)^2*sin(alpha)^2*sin(alpha - pi/4)^2 + r^2*tan(alpha/2)^4*sin(alpha)^2*sin(alpha - pi/4)^2 - 2^(1/2)*R*r*cos(alpha)^2 - 2*r^2*tan(alpha/2)^2*cos(alpha)^3*sin(alpha) - r^2*tan(alpha/2)^4*cos(alpha)^3*sin(alpha) + 2^(1/2)*r*x*cos(alpha)^2 + 2^(1/2)*R*r*cos(alpha)*sin(alpha) - 2*2^(1/2)*R*r*tan(alpha/2)^2*cos(alpha)^2 - 2^(1/2)*R*r*tan(alpha/2)^4*cos(alpha)^2 - 2^(1/2)*r*x*cos(alpha)*sin(alpha) + 2*2^(1/2)*r*x*tan(alpha/2)^2*cos(alpha)^2 + 2^(1/2)*r*x*tan(alpha/2)^4*cos(alpha)^2 - 4*r*y*tan(alpha/2)^2*sin(alpha)*sin(alpha - pi/4) - 2*r*y*tan(alpha/2)^4*sin(alpha)*sin(alpha - pi/4) + 2*2^(1/2)*R*r*tan(alpha/2)^2*cos(alpha)*sin(alpha) + 2^(1/2)*R*r*tan(alpha/2)^4*cos(alpha)*sin(alpha) - 2*2^(1/2)*r*x*tan(alpha/2)^2*cos(alpha)*sin(alpha) - 2^(1/2)*r*x*tan(alpha/2)^4*cos(alpha)*sin(alpha)))^(1/2) + 2^(1/2)*l*r - 4*R*l*tan(alpha/2)^2 - 2*R*l*tan(alpha/2)^4 + 4*l*x*tan(alpha/2)^2 + 2*l*x*tan(alpha/2)^4 - 2*2^(1/2)*l*r*tan(alpha/2)^2 + 2*2^(1/2)*l*r*tan(alpha/2)^3 + 2^(1/2)*l*r*tan(alpha/2)^4 - 2*2^(1/2)*l*r*tan(alpha/2)))/(r^2*cos(alpha)^4 - 4*l*z - 4*R*x + 4*R^2*tan(alpha/2)^2 + 2*R^2*tan(alpha/2)^4 + 2*R^2 + 4*l^2*tan(alpha/2)^2 + 2*l^2*tan(alpha/2)^4 - 4*m^2*tan(alpha/2)^2 - 2*m^2*tan(alpha/2)^4 + 2*l^2 + 4*x^2*tan(alpha/2)^2 + 2*x^2*tan(alpha/2)^4 - 2*m^2 + 4*y^2*tan(alpha/2)^2 + 2*y^2*tan(alpha/2)^4 + 4*z^2*tan(alpha/2)^2 + 2*z^2*tan(alpha/2)^4 + 2*x^2 + 2*y^2 + 2*z^2 - 2*r^2*cos(alpha)^3*sin(alpha) + r^2*cos(alpha)^2*sin(alpha)^2 + 2*r^2*sin(alpha)^2*sin(alpha - pi/4)^2 - 8*R*x*tan(alpha/2)^2 - 4*R*x*tan(alpha/2)^4 - 8*l*z*tan(alpha/2)^2 - 4*l*z*tan(alpha/2)^4 + 2*r^2*tan(alpha/2)^2*cos(alpha)^4 + r^2*tan(alpha/2)^4*cos(alpha)^4 - 4*r*y*sin(alpha)*sin(alpha - pi/4) + 2*r^2*tan(alpha/2)^2*cos(alpha)^2*sin(alpha)^2 + r^2*tan(alpha/2)^4*cos(alpha)^2*sin(alpha)^2 + 4*r^2*tan(alpha/2)^2*sin(alpha)^2*sin(alpha - pi/4)^2 + 2*r^2*tan(alpha/2)^4*sin(alpha)^2*sin(alpha - pi/4)^2 - 2*2^(1/2)*R*r*cos(alpha)^2 - 4*r^2*tan(alpha/2)^2*cos(alpha)^3*sin(alpha) - 2*r^2*tan(alpha/2)^4*cos(alpha)^3*sin(alpha) + 2*2^(1/2)*r*x*cos(alpha)^2 + 2*2^(1/2)*R*r*cos(alpha)*sin(alpha) - 4*2^(1/2)*R*r*tan(alpha/2)^2*cos(alpha)^2 - 2*2^(1/2)*R*r*tan(alpha/2)^4*cos(alpha)^2 - 2*2^(1/2)*r*x*cos(alpha)*sin(alpha) + 4*2^(1/2)*r*x*tan(alpha/2)^2*cos(alpha)^2 + 2*2^(1/2)*r*x*tan(alpha/2)^4*cos(alpha)^2 - 8*r*y*tan(alpha/2)^2*sin(alpha)*sin(alpha - pi/4) - 4*r*y*tan(alpha/2)^4*sin(alpha)*sin(alpha - pi/4) + 4*2^(1/2)*R*r*tan(alpha/2)^2*cos(alpha)*sin(alpha) + 2*2^(1/2)*R*r*tan(alpha/2)^4*cos(alpha)*sin(alpha) - 4*2^(1/2)*r*x*tan(alpha/2)^2*cos(alpha)*sin(alpha) - 2*2^(1/2)*r*x*tan(alpha/2)^4*cos(alpha)*sin(alpha))) -2*atan((2*(2*R*l - 2*l*x + ((4*l*x - 4*R*l + 2*2^(1/2)*l*r - 8*R*l*tan(alpha/2)^2 - 4*R*l*tan(alpha/2)^4 + 8*l*x*tan(alpha/2)^2 + 4*l*x*tan(alpha/2)^4 - 4*2^(1/2)*l*r*tan(alpha/2)^2 + 4*2^(1/2)*l*r*tan(alpha/2)^3 + 2*2^(1/2)*l*r*tan(alpha/2)^4 - 4*2^(1/2)*l*r*tan(alpha/2))^2/4 - ((r^2*cos(alpha)^4)/2 - 2*l*z - 2*R*x + 2*R^2*tan(alpha/2)^2 + R^2*tan(alpha/2)^4 + R^2 + 2*l^2*tan(alpha/2)^2 + l^2*tan(alpha/2)^4 - 2*m^2*tan(alpha/2)^2 - m^2*tan(alpha/2)^4 + l^2 + 2*x^2*tan(alpha/2)^2 + x^2*tan(alpha/2)^4 - m^2 + 2*y^2*tan(alpha/2)^2 + y^2*tan(alpha/2)^4 + 2*z^2*tan(alpha/2)^2 + z^2*tan(alpha/2)^4 + x^2 + y^2 + z^2 - r^2*cos(alpha)^3*sin(alpha) + (r^2*cos(alpha)^2*sin(alpha)^2)/2 + r^2*sin(alpha)^2*sin(alpha - pi/4)^2 - 4*R*x*tan(alpha/2)^2 - 2*R*x*tan(alpha/2)^4 - 4*l*z*tan(alpha/2)^2 - 2*l*z*tan(alpha/2)^4 + r^2*tan(alpha/2)^2*cos(alpha)^4 + (r^2*tan(alpha/2)^4*cos(alpha)^4)/2 - 2*r*y*sin(alpha)*sin(alpha - pi/4) + r^2*tan(alpha/2)^2*cos(alpha)^2*sin(alpha)^2 + (r^2*tan(alpha/2)^4*cos(alpha)^2*sin(alpha)^2)/2 + 2*r^2*tan(alpha/2)^2*sin(alpha)^2*sin(alpha - pi/4)^2 + r^2*tan(alpha/2)^4*sin(alpha)^2*sin(alpha - pi/4)^2 - 2^(1/2)*R*r*cos(alpha)^2 - 2*r^2*tan(alpha/2)^2*cos(alpha)^3*sin(alpha) - r^2*tan(alpha/2)^4*cos(alpha)^3*sin(alpha) + 2^(1/2)*r*x*cos(alpha)^2 + 2^(1/2)*R*r*cos(alpha)*sin(alpha) - 2*2^(1/2)*R*r*tan(alpha/2)^2*cos(alpha)^2 - 2^(1/2)*R*r*tan(alpha/2)^4*cos(alpha)^2 - 2^(1/2)*r*x*cos(alpha)*sin(alpha) + 2*2^(1/2)*r*x*tan(alpha/2)^2*cos(alpha)^2 + 2^(1/2)*r*x*tan(alpha/2)^4*cos(alpha)^2 - 4*r*y*tan(alpha/2)^2*sin(alpha)*sin(alpha - pi/4) - 2*r*y*tan(alpha/2)^4*sin(alpha)*sin(alpha - pi/4) + 2*2^(1/2)*R*r*tan(alpha/2)^2*cos(alpha)*sin(alpha) + 2^(1/2)*R*r*tan(alpha/2)^4*cos(alpha)*sin(alpha) - 2*2^(1/2)*r*x*tan(alpha/2)^2*cos(alpha)*sin(alpha) - 2^(1/2)*r*x*tan(alpha/2)^4*cos(alpha)*sin(alpha))*(2*l*z - 2*R*x + (r^2*cos(alpha)^4)/2 + 2*R^2*tan(alpha/2)^2 + R^2*tan(alpha/2)^4 + R^2 + 2*l^2*tan(alpha/2)^2 + l^2*tan(alpha/2)^4 - 2*m^2*tan(alpha/2)^2 - m^2*tan(alpha/2)^4 + l^2 + 2*x^2*tan(alpha/2)^2 + x^2*tan(alpha/2)^4 - m^2 + 2*y^2*tan(alpha/2)^2 + y^2*tan(alpha/2)^4 + 2*z^2*tan(alpha/2)^2 + z^2*tan(alpha/2)^4 + x^2 + y^2 + z^2 - r^2*cos(alpha)^3*sin(alpha) + (r^2*cos(alpha)^2*sin(alpha)^2)/2 + r^2*sin(alpha)^2*sin(alpha - pi/4)^2 - 4*R*x*tan(alpha/2)^2 - 2*R*x*tan(alpha/2)^4 + 4*l*z*tan(alpha/2)^2 + 2*l*z*tan(alpha/2)^4 + r^2*tan(alpha/2)^2*cos(alpha)^4 + (r^2*tan(alpha/2)^4*cos(alpha)^4)/2 - 2*r*y*sin(alpha)*sin(alpha - pi/4) + r^2*tan(alpha/2)^2*cos(alpha)^2*sin(alpha)^2 + (r^2*tan(alpha/2)^4*cos(alpha)^2*sin(alpha)^2)/2 + 2*r^2*tan(alpha/2)^2*sin(alpha)^2*sin(alpha - pi/4)^2 + r^2*tan(alpha/2)^4*sin(alpha)^2*sin(alpha - pi/4)^2 - 2^(1/2)*R*r*cos(alpha)^2 - 2*r^2*tan(alpha/2)^2*cos(alpha)^3*sin(alpha) - r^2*tan(alpha/2)^4*cos(alpha)^3*sin(alpha) + 2^(1/2)*r*x*cos(alpha)^2 + 2^(1/2)*R*r*cos(alpha)*sin(alpha) - 2*2^(1/2)*R*r*tan(alpha/2)^2*cos(alpha)^2 - 2^(1/2)*R*r*tan(alpha/2)^4*cos(alpha)^2 - 2^(1/2)*r*x*cos(alpha)*sin(alpha) + 2*2^(1/2)*r*x*tan(alpha/2)^2*cos(alpha)^2 + 2^(1/2)*r*x*tan(alpha/2)^4*cos(alpha)^2 - 4*r*y*tan(alpha/2)^2*sin(alpha)*sin(alpha - pi/4) - 2*r*y*tan(alpha/2)^4*sin(alpha)*sin(alpha - pi/4) + 2*2^(1/2)*R*r*tan(alpha/2)^2*cos(alpha)*sin(alpha) + 2^(1/2)*R*r*tan(alpha/2)^4*cos(alpha)*sin(alpha) - 2*2^(1/2)*r*x*tan(alpha/2)^2*cos(alpha)*sin(alpha) - 2^(1/2)*r*x*tan(alpha/2)^4*cos(alpha)*sin(alpha)))^(1/2) - 2^(1/2)*l*r + 4*R*l*tan(alpha/2)^2 + 2*R*l*tan(alpha/2)^4 - 4*l*x*tan(alpha/2)^2 - 2*l*x*tan(alpha/2)^4 + 2*2^(1/2)*l*r*tan(alpha/2)^2 - 2*2^(1/2)*l*r*tan(alpha/2)^3 - 2^(1/2)*l*r*tan(alpha/2)^4 + 2*2^(1/2)*l*r*tan(alpha/2)))/(r^2*cos(alpha)^4 - 4*l*z - 4*R*x + 4*R^2*tan(alpha/2)^2 + 2*R^2*tan(alpha/2)^4 + 2*R^2 + 4*l^2*tan(alpha/2)^2 + 2*l^2*tan(alpha/2)^4 - 4*m^2*tan(alpha/2)^2 - 2*m^2*tan(alpha/2)^4 + 2*l^2 + 4*x^2*tan(alpha/2)^2 + 2*x^2*tan(alpha/2)^4 - 2*m^2 + 4*y^2*tan(alpha/2)^2 + 2*y^2*tan(alpha/2)^4 + 4*z^2*tan(alpha/2)^2 + 2*z^2*tan(alpha/2)^4 + 2*x^2 + 2*y^2 + 2*z^2 - 2*r^2*cos(alpha)^3*sin(alpha) + r^2*cos(alpha)^2*sin(alpha)^2 + 2*r^2*sin(alpha)^2*sin(alpha - pi/4)^2 - 8*R*x*tan(alpha/2)^2 - 4*R*x*tan(alpha/2)^4 - 8*l*z*tan(alpha/2)^2 - 4*l*z*tan(alpha/2)^4 + 2*r^2*tan(alpha/2)^2*cos(alpha)^4 + r^2*tan(alpha/2)^4*cos(alpha)^4 - 4*r*y*sin(alpha)*sin(alpha - pi/4) + 2*r^2*tan(alpha/2)^2*cos(alpha)^2*sin(alpha)^2 + r^2*tan(alpha/2)^4*cos(alpha)^2*sin(alpha)^2 + 4*r^2*tan(alpha/2)^2*sin(alpha)^2*sin(alpha - pi/4)^2 + 2*r^2*tan(alpha/2)^4*sin(alpha)^2*sin(alpha - pi/4)^2 - 2*2^(1/2)*R*r*cos(alpha)^2 - 4*r^2*tan(alpha/2)^2*cos(alpha)^3*sin(alpha) - 2*r^2*tan(alpha/2)^4*cos(alpha)^3*sin(alpha) + 2*2^(1/2)*r*x*cos(alpha)^2 + 2*2^(1/2)*R*r*cos(alpha)*sin(alpha) - 4*2^(1/2)*R*r*tan(alpha/2)^2*cos(alpha)^2 - 2*2^(1/2)*R*r*tan(alpha/2)^4*cos(alpha)^2 - 2*2^(1/2)*r*x*cos(alpha)*sin(alpha) + 4*2^(1/2)*r*x*tan(alpha/2)^2*cos(alpha)^2 + 2*2^(1/2)*r*x*tan(alpha/2)^4*cos(alpha)^2 - 8*r*y*tan(alpha/2)^2*sin(alpha)*sin(alpha - pi/4) - 4*r*y*tan(alpha/2)^4*sin(alpha)*sin(alpha - pi/4) + 4*2^(1/2)*R*r*tan(alpha/2)^2*cos(alpha)*sin(alpha) + 2*2^(1/2)*R*r*tan(alpha/2)^4*cos(alpha)*sin(alpha) - 4*2^(1/2)*r*x*tan(alpha/2)^2*cos(alpha)*sin(alpha) - 2*2^(1/2)*r*x*tan(alpha/2)^4*cos(alpha)*sin(alpha))) simple(d) simplify: 2*atan((2*cos(alpha/2)^4*(2*l*x - 2*R*l + ((16*l^2*(2*R - 2*x - 2^(1/2)*r*cos(alpha)^2 + (2^(1/2)*r*sin(2*alpha))/2)^2)/(cos(alpha) + 1)^4 - ((2*R^2 - 4*l*z - r^2*sin(2*alpha) - 4*R*x + 2*l^2 - 2*m^2 + r^2 + 2*x^2 + 2*y^2 + 2*z^2 - 2^(1/2)*R*r + 2*r*y*sin(pi/4 + 2*alpha) + 2^(1/2)*r*x - 2^(1/2)*r*y - 2^(1/2)*R*r*cos(2*alpha) + 2^(1/2)*R*r*sin(2*alpha) + 2^(1/2)*r*x*cos(2*alpha) - 2^(1/2)*r*x*sin(2*alpha))*(4*l*z - 4*R*x - r^2*sin(2*alpha) + 2*R^2 + 2*l^2 - 2*m^2 + r^2 + 2*x^2 + 2*y^2 + 2*z^2 - 2^(1/2)*R*r + 2*r*y*sin(pi/4 + 2*alpha) + 2^(1/2)*r*x - 2^(1/2)*r*y - 2^(1/2)*R*r*cos(2*alpha) + 2^(1/2)*R*r*sin(2*alpha) + 2^(1/2)*r*x*cos(2*alpha) - 2^(1/2)*r*x*sin(2*alpha)))/(4*cos(alpha/2)^8))^(1/2) + 2^(1/2)*l*r - 4*R*l*tan(alpha/2)^2 - 2*R*l*tan(alpha/2)^4 + 4*l*x*tan(alpha/2)^2 + 2*l*x*tan(alpha/2)^4 - 2*2^(1/2)*l*r*tan(alpha/2)^2 + 2*2^(1/2)*l*r*tan(alpha/2)^3 + 2^(1/2)*l*r*tan(alpha/2)^4 - 2*2^(1/2)*l*r*tan(alpha/2)))/(2*R^2 - 4*l*z - r^2*sin(2*alpha) - 4*R*x + 2*l^2 - 2*m^2 + r^2 + 2*x^2 + 2*y^2 + 2*z^2 - 2^(1/2)*R*r + 2*r*y*sin(pi/4 + 2*alpha) + 2^(1/2)*r*x - 2^(1/2)*r*y - 2^(1/2)*R*r*cos(2*alpha) + 2^(1/2)*R*r*sin(2*alpha) + 2^(1/2)*r*x*cos(2*alpha) - 2^(1/2)*r*x*sin(2*alpha))) -2*atan((2*cos(alpha/2)^4*(2*R*l - 2*l*x + ((16*l^2*(2*R - 2*x - 2^(1/2)*r*cos(alpha)^2 + (2^(1/2)*r*sin(2*alpha))/2)^2)/(cos(alpha) + 1)^4 - ((2*R^2 - 4*l*z - r^2*sin(2*alpha) - 4*R*x + 2*l^2 - 2*m^2 + r^2 + 2*x^2 + 2*y^2 + 2*z^2 - 2^(1/2)*R*r + 2*r*y*sin(pi/4 + 2*alpha) + 2^(1/2)*r*x - 2^(1/2)*r*y - 2^(1/2)*R*r*cos(2*alpha) + 2^(1/2)*R*r*sin(2*alpha) + 2^(1/2)*r*x*cos(2*alpha) - 2^(1/2)*r*x*sin(2*alpha))*(4*l*z - 4*R*x - r^2*sin(2*alpha) + 2*R^2 + 2*l^2 - 2*m^2 + r^2 + 2*x^2 + 2*y^2 + 2*z^2 - 2^(1/2)*R*r + 2*r*y*sin(pi/4 + 2*alpha) + 2^(1/2)*r*x - 2^(1/2)*r*y - 2^(1/2)*R*r*cos(2*alpha) + 2^(1/2)*R*r*sin(2*alpha) + 2^(1/2)*r*x*cos(2*alpha) - 2^(1/2)*r*x*sin(2*alpha)))/(4*cos(alpha/2)^8))^(1/2) - 2^(1/2)*l*r + 4*R*l*tan(alpha/2)^2 + 2*R*l*tan(alpha/2)^4 - 4*l*x*tan(alpha/2)^2 - 2*l*x*tan(alpha/2)^4 + 2*2^(1/2)*l*r*tan(alpha/2)^2 - 2*2^(1/2)*l*r*tan(alpha/2)^3 - 2^(1/2)*l*r*tan(alpha/2)^4 + 2*2^(1/2)*l*r*tan(alpha/2)))/(2*R^2 - 4*l*z - r^2*sin(2*alpha) - 4*R*x + 2*l^2 - 2*m^2 + r^2 + 2*x^2 + 2*y^2 + 2*z^2 - 2^(1/2)*R*r + 2*r*y*sin(pi/4 + 2*alpha) + 2^(1/2)*r*x - 2^(1/2)*r*y - 2^(1/2)*R*r*cos(2*alpha) + 2^(1/2)*R*r*sin(2*alpha) + 2^(1/2)*r*x*cos(2*alpha) - 2^(1/2)*r*x*sin(2*alpha))) |
7楼2012-05-21 14:45:09
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