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📁 本程序所反应的是在测量中被广泛应用的全球定位系统(Global Position System)在空间中的形象以及基本的工作原理。GPS由三部分组成:空间部分、地面控制系统以及用户部分。
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yyy=-(1/2*aa1*cc2/(aa1^2*cc2^2+bb2^2*cc1^2+aa1^2*bb2^2+cc2^2*bb1^2+aa2^2*cc1^2+bb1^2*aa2^2-2*aa2*aa1*cc2*cc1-2*bb2*cc2*bb1*cc1-2*aa1*bb2*bb1*aa2)*(-2*dd1*cc1*bb2^2-2*dd1*cc1*aa2^2-2*bb1^2*dd2*cc2-2*dd2*cc2*aa1^2+2*dd2*bb2*bb1*cc1+2*bb2*cc2*bb1*dd1+2*aa2*aa1*dd2*cc1+2*aa2*aa1*cc2*dd1+2*(-aa1^2*bb2^4*dd1^2+aa1^4*bb2^4*r^2-aa1^4*bb2^2*dd2^2+bb1^4*aa2^4*r^2-bb1^4*aa2^2*dd2^2-bb1^2*aa2^4*dd1^2+aa1^4*cc2^2*r^2*bb2^2-aa1^2*cc2^2*bb2^2*dd1^2+bb2^4*cc1^2*r^2*aa1^2-bb2^2*cc1^2*aa1^2*dd2^2-aa1^2*bb2^2*dd2^2*bb1^2-aa1^2*bb2^2*aa2^2*dd1^2+cc2^2*bb1^4*r^2*aa2^2-cc2^2*bb1^2*aa2^2*dd1^2+aa2^4*cc1^2*r^2*bb1^2-aa2^2*cc1^2*dd2^2*bb1^2-bb1^2*aa2^2*aa1^2*dd2^2-bb1^2*aa2^2*bb2^2*dd1^2+aa1^2*cc2^2*r^2*aa2^2*bb1^2-2*aa1^3*cc2^2*r^2*aa2*bb2*bb1+bb2^2*cc1^2*r^2*aa2^2*bb1^2+2*dd1*cc1*bb2^2*dd2*cc2*aa1^2+2*dd1*cc1*aa2^2*bb1^2*dd2*cc2+2*dd2^2*bb2*bb1*cc1^2*aa2*aa1-4*dd2*bb2*bb1*cc1*aa2*aa1*cc2*dd1+2*bb2*cc2^2*bb1*dd1^2*aa2*aa1-2*bb2^3*cc1^2*r^2*aa2*aa1*bb1+6*aa1^2*bb2^2*r^2*aa2^2*bb1^2+2*aa1^3*bb2^2*aa2*dd2*dd1-4*aa1^3*bb2^3*r^2*aa2*bb1+2*aa1^2*bb2^3*dd2*bb1*dd1+cc2^2*bb1^2*r^2*aa1^2*bb2^2-2*cc2^2*bb1^3*r^2*aa2*aa1*bb2+aa2^2*cc1^2*r^2*aa1^2*bb2^2-2*aa2^3*cc1^2*r^2*aa1*bb2*bb1+2*bb1^2*aa2^3*aa1*dd2*dd1-4*bb1^3*aa2^3*r^2*aa1*bb2+2*bb1^3*aa2^2*dd2*bb2*dd1-2*aa2^3*aa1*cc2*cc1*r^2*bb1^2-2*aa2*aa1^3*cc2*cc1*r^2*bb2^2+4*aa2^2*aa1^2*cc2*cc1*r^2*bb2*bb1-2*bb2*cc2*bb1^3*cc1*r^2*aa2^2-2*bb2^3*cc2*bb1*cc1*r^2*aa1^2+4*bb2^2*cc2*bb1^2*cc1*r^2*aa2*aa1-4*aa1^2*bb2*bb1*aa2^2*dd2*dd1+2*aa1^3*bb2*bb1*aa2*dd2^2+2*aa1*bb2^3*bb1*aa2*dd1^2+2*aa1*bb2*bb1^3*aa2*dd2^2+2*aa1*bb2*bb1*aa2^3*dd1^2-4*aa1*bb2^2*bb1^2*aa2*dd2*dd1)^(1/2))+aa1*dd2-1/2*cc1/(aa1^2*cc2^2+bb2^2*cc1^2+aa1^2*bb2^2+cc2^2*bb1^2+aa2^2*cc1^2+bb1^2*aa2^2-2*aa2*aa1*cc2*cc1-2*bb2*cc2*bb1*cc1-2*aa1*bb2*bb1*aa2)*(-2*dd1*cc1*bb2^2-2*dd1*cc1*aa2^2-2*bb1^2*dd2*cc2-2*dd2*cc2*aa1^2+2*dd2*bb2*bb1*cc1+2*bb2*cc2*bb1*dd1+2*aa2*aa1*dd2*cc1+2*aa2*aa1*cc2*dd1+2*
(-aa1^2*bb2^4*dd1^2+aa1^4*bb2^4*r^2-aa1^4*bb2^2*dd2^2+bb1^4*aa2^4*r^2-bb1^4*aa2^2*dd2^2-bb1^2*aa2^4*dd1^2+aa1^4*cc2^2*r^2*bb2^2-aa1^2*cc2^2*bb2^2*dd1^2+bb2^4*cc1^2*r^2*aa1^2-bb2^2*cc1^2*aa1^2*dd2^2-aa1^2*bb2^2*dd2^2*bb1^2-aa1^2*bb2^2*aa2^2*dd1^2+cc2^2*bb1^4*r^2*aa2^2-cc2^2*bb1^2*aa2^2*dd1^2+aa2^4*cc1^2*r^2*bb1^2-aa2^2*cc1^2*dd2^2*bb1^2-bb1^2*aa2^2*aa1^2*dd2^2-bb1^2*aa2^2*bb2^2*dd1^2+aa1^2*cc2^2*r^2*aa2^2*bb1^2-2*aa1^3*cc2^2*r^2*aa2*bb2*bb1+bb2^2*cc1^2*r^2*aa2^2*bb1^2+2*dd1*cc1*bb2^2*dd2*cc2*aa1^2+2*dd1*cc1*aa2^2*bb1^2*dd2*cc2+2*dd2^2*bb2*bb1*cc1^2*aa2*aa1-4*dd2*bb2*bb1*cc1*aa2*aa1*cc2*dd1+2*bb2*cc2^2*bb1*dd1^2*aa2*aa1-2*bb2^3*cc1^2*r^2*aa2*aa1*bb1+6*aa1^2*bb2^2*r^2*aa2^2*bb1^2+2*aa1^3*bb2^2*aa2*dd2*dd1-4*aa1^3*bb2^3*r^2*aa2*bb1+2*aa1^2*bb2^3*dd2*bb1*dd1+cc2^2*bb1^2*r^2*aa1^2*bb2^2-2*cc2^2*bb1^3*r^2*aa2*aa1*bb2+aa2^2*cc1^2*r^2*aa1^2*bb2^2-2*aa2^3*cc1^2*r^2*aa1*bb2*bb1+2*bb1^2*aa2^3*aa1*dd2*dd1-4*bb1^3*aa2^3*r^2*aa1*bb2+2*bb1^3*aa2^2*dd2*bb2*dd1-2*aa2^3*aa1*cc2*cc1*r^2*bb1^2-2*aa2*aa1^3*cc2*cc1*r^2*bb2^2+4*aa2^2*aa1^2*cc2*cc1*r^2*bb2*bb1-2*bb2*cc2*bb1^3*cc1*r^2*aa2^2-2*bb2^3*cc2*bb1*cc1*r^2*aa1^2+4*bb2^2*cc2*bb1^2*cc1*r^2*aa2*aa1-4*aa1^2*bb2*bb1*aa2^2*dd2*dd1+2*aa1^3*bb2*bb1*aa2*dd2^2+2*aa1*bb2^3*bb1*aa2*dd1^2+2*aa1*bb2*bb1^3*aa2*dd2^2+2*aa1*bb2*bb1*aa2^3*dd1^2-4*aa1*bb2^2*bb1^2*aa2*dd2*dd1)^(1/2))*aa2-dd1*aa2)/(aa1*bb2-bb1*aa2)
bian111=-2*bb2^3*cc2*bb1*cc1*r^2*aa1^2+4*bb2^2*cc2*bb1^2*cc1*r^2*aa2*aa1-4*aa1^2*bb2*bb1*aa2^2*dd2*dd1+2*aa1^3*bb2*bb1*aa2*dd2^2+2*aa1*bb2^3*bb1*aa2*dd1^2+2*aa1*bb2*bb1^3*aa2*dd2^2+2*aa1*bb2*bb1*aa2^3*dd1^2-4*aa1*bb2^2*bb1^2*aa2*dd2*dd1
bian11=-4*aa1^3*bb2^3*r^2*aa2*bb1+2*aa1^2*bb2^3*dd2*bb1*dd1+cc2^2*bb1^2*r^2*aa1^2*bb2^2-2*cc2^2*bb1^3*r^2*aa2*aa1*bb2+aa2^2*cc1^2*r^2*aa1^2*bb2^2-2*aa2^3*cc1^2*r^2*aa1*bb2*bb1+2*bb1^2*aa2^3*aa1*dd2*dd1-4*bb1^3*aa2^3*r^2*aa1*bb2+2*bb1^3*aa2^2*dd2*bb2*dd1-2*aa2^3*aa1*cc2*cc1*r^2*bb1^2-2*aa2*aa1^3*cc2*cc1*r^2*bb2^2+4*aa2^2*aa1^2*cc2*cc1*r^2*bb2*bb1-2*bb2*cc2*bb1^3*cc1*r^2*aa2^2+bian111
bian121=2*dd1*cc1*aa2^2*bb1^2*dd2*cc2+2*dd2^2*bb2*bb1*cc1^2*aa2*aa1-4*dd2*bb2*bb1*cc1*aa2*aa1*cc2*dd1+2*bb2*cc2^2*bb1*dd1^2*aa2*aa1-2*bb2^3*cc1^2*r^2*aa2*aa1*bb1+6*aa1^2*bb2^2*r^2*aa2^2*bb1^2+2*aa1^3*bb2^2*aa2*dd2*dd1
bian12=-bb2^2*cc1^2*aa1^2*dd2^2-aa1^2*bb2^2*dd2^2*bb1^2-aa1^2*bb2^2*aa2^2*dd1^2+cc2^2*bb1^4*r^2*aa2^2-cc2^2*bb1^2*aa2^2*dd1^2+aa2^4*cc1^2*r^2*bb1^2-aa2^2*cc1^2*dd2^2*bb1^2-bb1^2*aa2^2*aa1^2*dd2^2-bb1^2*aa2^2*bb2^2*dd1^2+aa1^2*cc2^2*r^2*aa2^2*bb1^2-2*aa1^3*cc2^2*r^2*aa2*bb2*bb1+bb2^2*cc1^2*r^2*aa2^2*bb1^2+2*dd1*cc1*bb2^2*dd2*cc2*aa1^2+bian121
bian1=-aa1^2*bb2^4*dd1^2+aa1^4*bb2^4*r^2-aa1^4*bb2^2*dd2^2+bb1^4*aa2^4*r^2-bb1^4*aa2^2*dd2^2-bb1^2*aa2^4*dd1^2+aa1^4*cc2^2*r^2*bb2^2-aa1^2*cc2^2*bb2^2*dd1^2+bb2^4*cc1^2*r^2*aa1^2+bian12+bian11


yyy=-(1/2*aa1*cc2/(aa1^2*cc2^2+bb2^2*cc1^2+aa1^2*bb2^2+cc2^2*bb1^2+aa2^2*cc1^2+bb1^2*aa2^2-2*aa2*aa1*cc2*cc1-2*bb2*cc2*bb1*cc1-2*aa1*bb2*bb1*aa2)*(-2*dd1*cc1*bb2^2-2*dd1*cc1*aa2^2-2*bb1^2*dd2*cc2-2*dd2*cc2*aa1^2+2*dd2*bb2*bb1*cc1+2*bb2*cc2*bb1*dd1+2*aa2*aa1*dd2*cc1+2*aa2*aa1*cc2*dd1+2*(-aa1^2*bb2^4*dd1^2+aa1^4*bb2^4*r^2-aa1^4*bb2^2*dd2^2+bb1^4*aa2^4*r^2-bb1^4*aa2^2*dd2^2-bb1^2*aa2^4*dd1^2+aa1^4*cc2^2*r^2*bb2^2-aa1^2*cc2^2*bb2^2*dd1^2+bb2^4*cc1^2*r^2*aa1^2-bb2^2*cc1^2*aa1^2*dd2^2-aa1^2*bb2^2*dd2^2*bb1^2-aa1^2*bb2^2*aa2^2*dd1^2+cc2^2*bb1^4*r^2*aa2^2-cc2^2*bb1^2*aa2^2*dd1^2+aa2^4*cc1^2*r^2*bb1^2-aa2^2*cc1^2*dd2^2*bb1^2-bb1^2*aa2^2*aa1^2*dd2^2-bb1^2*aa2^2*bb2^2*dd1^2+aa1^2*cc2^2*r^2*aa2^2*bb1^2-2*aa1^3*cc2^2*r^2*aa2*bb2*bb1+bb2^2*cc1^2*r^2*aa2^2*bb1^2+2*dd1*cc1*bb2^2*dd2*cc2*aa1^2+2*dd1*cc1*aa2^2*bb1^2*dd2*cc2+2*dd2^2*bb2*bb1*cc1^2*aa2*aa1-4*dd2*bb2*bb1*cc1*aa2*aa1*cc2*dd1+2*bb2*cc2^2*bb1*dd1^2*aa2*aa1-2*bb2^3*cc1^2*r^2*aa2*aa1*bb1+6*aa1^2*bb2^2*r^2*aa2^2*bb1^2+2*aa1^3*bb2^2*aa2*dd2*dd1-4*aa1^3*bb2^3*r^2*aa2*bb1+2*aa1^2*bb2^3*dd2*bb1*dd1+cc2^2*bb1^2*r^2*aa1^2*bb2^2-2*cc2^2*bb1^3*r^2*aa2*aa1*bb2+aa2^2*cc1^2*r^2*aa1^2*bb2^2-2*aa2^3*cc1^2*r^2*aa1*bb2*bb1+2*bb1^2*aa2^3*aa1*dd2*dd1-4*bb1^3*aa2^3*r^2*aa1*bb2+2*bb1^3*aa2^2*dd2*bb2*dd1-2*aa2^3*aa1*cc2*cc1*r^2*bb1^2-2*aa2*aa1^3*cc2*cc1*r^2*bb2^2+4*aa2^2*aa1^2*cc2*cc1*r^2*bb2*bb1-2*bb2*cc2*bb1^3*cc1*r^2*aa2^2-2*bb2^3*cc2*bb1*cc1*r^2*aa1^2+4*bb2^2*cc2*bb1^2*cc1*r^2*aa2*aa1-4*aa1^2*bb2*bb1*aa2^2*dd2*dd1+2*aa1^3*bb2*bb1*aa2*dd2^2+2*aa1*bb2^3*bb1*aa2*dd1^2+2*aa1*bb2*bb1^3*aa2*dd2^2+2*aa1*bb2*bb1*aa2^3*dd1^2-4*aa1*bb2^2*bb1^2*aa2*dd2*dd1)^(1/2))+aa1*dd2-1/2*cc1/(aa1^2*cc2^2+bb2^2*cc1^2+aa1^2*bb2^2+cc2^2*bb1^2+aa2^2*cc1^2+bb1^2*aa2^2-2*aa2*aa1*cc2*cc1-2*bb2*cc2*bb1*cc1-2*aa1*bb2*bb1*aa2)*
(-2*dd1*cc1*bb2^2-2*dd1*cc1*aa2^2-2*bb1^2*dd2*cc2-2*dd2*cc2*aa1^2+2*dd2*bb2*bb1*cc1+2*bb2*cc2*bb1*dd1+2*aa2*aa1*dd2*cc1+2*aa2*aa1*cc2*dd1+2*   bian1  ^(1/2))*aa2-dd1*aa2)/(aa1*bb2-bb1*aa2)
bian2=(-2*dd1*cc1*bb2^2-2*dd1*cc1*aa2^2-2*bb1^2*dd2*cc2-2*dd2*cc2*aa1^2+2*dd2*bb2*bb1*cc1+2*bb2*cc2*bb1*dd1+2*aa2*aa1*dd2*cc1+2*aa2*aa1*cc2*dd1+2*   bian1  ^(1/2))
yyy=-(1/2*aa1*cc2/(aa1^2*cc2^2+bb2^2*cc1^2+aa1^2*bb2^2+cc2^2*bb1^2+aa2^2*cc1^2+bb1^2*aa2^2-2*aa2*aa1*cc2*cc1-2*bb2*cc2*bb1*cc1-2*aa1*bb2*bb1*aa2)*(-2*dd1*cc1*bb2^2-2*dd1*cc1*aa2^2-2*bb1^2*dd2*cc2-2*dd2*cc2*aa1^2+2*dd2*bb2*bb1*cc1+2*bb2*cc2*bb1*dd1+2*aa2*aa1*dd2*cc1+2*aa2*aa1*cc2*dd1+2*   bian4  ^(1/2))   +aa1*dd2-1/2*cc1/  bian3  *   bian2   *aa2-dd1*aa2)/(aa1*bb2-bb1*aa2)
bian3=(aa1^2*cc2^2+bb2^2*cc1^2+aa1^2*bb2^2+cc2^2*bb1^2+aa2^2*cc1^2+bb1^2*aa2^2-2*aa2*aa1*cc2*cc1-2*bb2*cc2*bb1*cc1-2*aa1*bb2*bb1*aa2)
bian411=-4*bb1^3*aa2^3*r^2*aa1*bb2+2*bb1^3*aa2^2*dd2*bb2*dd1-2*aa2^3*aa1*cc2*cc1*r^2*bb1^2-2*aa2*aa1^3*cc2*cc1*r^2*bb2^2+4*aa2^2*aa1^2*cc2*cc1*r^2*bb2*bb1-2*bb2*cc2*bb1^3*cc1*r^2*aa2^2-2*bb2^3*cc2*bb1*cc1*r^2*aa1^2+4*bb2^2*cc2*bb1^2*cc1*r^2*aa2*aa1-4*aa1^2*bb2*bb1*aa2^2*dd2*dd1+2*aa1^3*bb2*bb1*aa2*dd2^2+2*aa1*bb2^3*bb1*aa2*dd1^2+2*aa1*bb2*bb1^3*aa2*dd2^2+2*aa1*bb2*bb1*aa2^3*dd1^2-4*aa1*bb2^2*bb1^2*aa2*dd2*dd1
bian41=-2*bb2^3*cc1^2*r^2*aa2*aa1*bb1+6*aa1^2*bb2^2*r^2*aa2^2*bb1^2+2*aa1^3*bb2^2*aa2*dd2*dd1-4*aa1^3*bb2^3*r^2*aa2*bb1+2*aa1^2*bb2^3*dd2*bb1*dd1+cc2^2*bb1^2*r^2*aa1^2*bb2^2-2*cc2^2*bb1^3*r^2*aa2*aa1*bb2+aa2^2*cc1^2*r^2*aa1^2*bb2^2-2*aa2^3*cc1^2*r^2*aa1*bb2*bb1+2*bb1^2*aa2^3*aa1*dd2*dd1+bian411
bian42=-2*aa1^3*cc2^2*r^2*aa2*bb2*bb1+bb2^2*cc1^2*r^2*aa2^2*bb1^2+2*dd1*cc1*bb2^2*dd2*cc2*aa1^2+2*dd1*cc1*aa2^2*bb1^2*dd2*cc2+2*dd2^2*bb2*bb1*cc1^2*aa2*aa1-4*dd2*bb2*bb1*cc1*aa2*aa1*cc2*dd1+2*bb2*cc2^2*bb1*dd1^2*aa2*aa1
bian4=-aa1^2*bb2^4*dd1^2+aa1^4*bb2^4*r^2-aa1^4*bb2^2*dd2^2+bb1^4*aa2^4*r^2-bb1^4*aa2^2*dd2^2-bb1^2*aa2^4*dd1^2+aa1^4*cc2^2*r^2*bb2^2-aa1^2*cc2^2*bb2^2*dd1^2+bb2^4*cc1^2*r^2*aa1^2-bb2^2*cc1^2*aa1^2*dd2^2-aa1^2*bb2^2*dd2^2*bb1^2-aa1^2*bb2^2*aa2^2*dd1^2+cc2^2*bb1^4*r^2*aa2^2-cc2^2*bb1^2*aa2^2*dd1^2+aa2^4*cc1^2*r^2*bb1^2-aa2^2*cc1^2*dd2^2*bb1^2-bb1^2*aa2^2*aa1^2*dd2^2-bb1^2*aa2^2*bb2^2*dd1^2+aa1^2*cc2^2*r^2*aa2^2*bb1^2+bian42+bian41








bian1=(aa1^2*cc2^2+bb2^2*cc1^2+aa1^2*bb2^2+cc2^2*bb1^2+aa2^2*cc1^2+bb1^2*aa2^2-2*aa2*aa1*cc2*cc1-2*bb2*cc2*bb1*cc1-2*aa1*bb2*bb1*aa2)

bian21=-4*aa1^2*bb2*bb1*aa2^2*dd2*dd1+2*aa1^3*bb2*bb1*aa2*dd2^2+2*aa1*bb2^3*bb1*aa2*dd1^2+2*aa1*bb2*bb1^3*aa2*dd2^2+2*aa1*bb2*bb1*aa2^3*dd1^2-4*aa1*bb2^2*bb1^2*aa2*dd2*dd1
bian22=-2*aa2*aa1^3*cc2*cc1*r^2*bb2^2+4*aa2^2*aa1^2*cc2*cc1*r^2*bb2*bb1-2*bb2*cc2*bb1^3*cc1*r^2*aa2^2-2*bb2^3*cc2*bb1*cc1*r^2*aa1^2+4*bb2^2*cc2*bb1^2*cc1*r^2*aa2*aa1
bian2=-2*dd1*cc1*bb2^2-2*dd1*cc1*aa2^2-2*bb1^2*dd2*cc2-2*dd2*cc2*aa1^2+2*dd2*bb2*bb1*cc1+2*bb2*cc2*bb1*dd1+2*aa2*aa1*dd2*cc1+2*aa2*aa1*cc2*dd1+2*(-aa1^2*bb2^4*dd1^2+aa1^4*bb2^4*r^2-aa1^4*bb2^2*dd2^2+bb1^4*aa2^4*r^2-bb1^4*aa2^2*dd2^2-bb1^2*aa2^4*dd1^2+aa1^4*cc2^2*r^2*bb2^2-aa1^2*cc2^2*bb2^2*dd1^2+bb2^4*cc1^2*r^2*aa1^2-bb2^2*cc1^2*aa1^2*dd2^2-aa1^2*bb2^2*dd2^2*bb1^2-aa1^2*bb2^2*aa2^2*dd1^2+cc2^2*bb1^4*r^2*aa2^2-cc2^2*bb1^2*aa2^2*dd1^2+aa2^4*cc1^2*r^2*bb1^2-aa2^2*cc1^2*dd2^2*bb1^2-bb1^2*aa2^2*aa1^2*dd2^2-bb1^2*aa2^2*bb2^2*dd1^2+aa1^2*cc2^2*r^2*aa2^2*bb1^2-2*aa1^3*cc2^2*r^2*aa2*bb2*bb1+bb2^2*cc1^2*r^2*aa2^2*bb1^2+2*dd1*cc1*bb2^2*dd2*cc2*aa1^2+2*dd1*cc1*aa2^2*bb1^2*dd2*cc2+2*dd2^2*bb2*bb1*cc1^2*aa2*aa1-4*dd2*bb2*bb1*cc1*aa2*aa1*cc2*dd1+2*bb2*cc2^2*bb1*dd1^2*aa2*aa1-2*bb2^3*cc1^2*r^2*aa2*aa1*bb1+6*aa1^2*bb2^2*r^2*aa2^2*bb1^2+2*aa1^3*bb2^2*aa2*dd2*dd1-4*aa1^3*bb2^3*r^2*aa2*bb1+2*aa1^2*bb2^3*dd2*bb1*dd1+cc2^2*bb1^2*r^2*aa1^2*bb2^2-2*cc2^2*bb1^3*r^2*aa2*aa1*bb2+aa2^2*cc1^2*r^2*aa1^2*bb2^2-2*aa2^3*cc1^2*r^2*aa1*bb2*bb1+2*bb1^2*aa2^3*aa1*dd2*dd1-4*bb1^3*aa2^3*r^2*aa1*bb2+2*bb1^3*aa2^2*dd2*bb2*dd1-2*aa2^3*aa1*cc2*cc1*r^2*bb1^2+bian22+bian21
zzz=1/2/   bian1   *bian2^(1/2))

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