2自由度弹簧质量模型 -- 状态方程--离散化 -- c++ -- matlab

 

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2020-05-04 10:08:10

Summary:

现代控制理论中的状态方程；状态方程的离散化、近似离散化；

C++算法实现；

实际应用：2自由度1/4车辆悬架垂向振动模型；

 

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建模： 弹簧阻尼系统，取系统处于静平衡的位置为原点，以消除重力的参与。O1-O2为水平基准，即m1的垂向位移为z1, m2的为z2，外部的激励输入为zr，当处于

静平衡时三者皆为零。

注意，这个系统在水平方向是不运动的，只在垂直方向运动， 当用于车辆的悬架模型时，外部激励来自路面的坑坑哇哇，所以图示中画了一个路面。

注意，z1，z2,zr总归是要在一个坐标系里衡量的，这里只需要一个一维坐标系，即，O1-O2为水平基准为基础，竖直向上为正，（虽然z1，z2画在了质量块的质心，嘿嘿）。

 

 

 

 

 

上面，u即外部输入，u=zr。（矩阵A,B都是常数矩阵，如果矩阵的元素随着系统的状态而改变，则是一个时变系统了，需要更精确地分析。）

然后，根据初始状态（x1=x2=x3=x4=0.0）即可解得方程了。由于要用到计算机系统中，所以需要将该状态方程进行离散化。

关于状态方程的意义，求解，离散化等可以参考《现代控制理论》：https://www.cnblogs.com/butterflybay/p/12825469.html

 

近似离散化：

https://wenku.baidu.com/view/ab37b916fbb069dc5022aaea998fcc22bdd14314.html

第k+1个周期与第k个周期的关系：

X(k+1) = G*X(k) + H*u,

G = I + A*T

H  = B*T

其中，T为标量，采样周期；（近似离散化的方法仅仅适用于很小的采样周期，例如0.00x秒）

I为单位矩阵；

 

精确离散化：

查书吧。

 

c++代码实现：

 

 

 

 

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Matlab中对状态方程的支持：

 

 

 

State-Space Models: https://ww2.mathworks.cn/help/control/ug/state-space-models.html

 

https://ww2.mathworks.cn/help/control/ref/ss.html

 

将连续状态空间方程进行离散：https://ww2.mathworks.cn/help/control/ref/c2d.html

 

https://ww2.mathworks.cn/help/control/ug/state-space-models.html

 

将符号替换为数值：subs函数：https://blog.csdn.net/guyuealian/article/details/53997490

状态转移矩阵计算：

https://blog.csdn.net/weixin_41394379/article/details/84581527

Other good:

https://wenku.baidu.com/view/e2dbb0020740be1e650e9ade.html

https://blog.csdn.net/qq_38693598/article/details/87877300

https://wenku.baidu.com/view/b73b5bd97f1922791688e824.html

 

我的小实验：

1)使用laplace变换，matlab符号计算来求解精确的符号解表达式：

syms k1 k2 c1 m1 m2 s T FS
A=[0 1 0 0;-k1/m1 -c1/m1 k1/m1 c1/m1;0 0 0 1;(k1+k2)/m2 c1/m2 -k1/m2 -c1/m2]
//离散化：
FS=inv(s*eye(4)-A)
LapI=ilaplace(FS,s,T)
res=simplify(LapI)
res =

[ k1*m1*symsum((root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T))/(2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 - c1*k2 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m1 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m2 + 4*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3*m1*m2), k, 1, 4) + c1*m1*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4) + c1*m2*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4) + m1*m2*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4),                                                                                                    c1*m1*symsum((root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T))/(2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 - c1*k2 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m1 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m2 + 4*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3*m1*m2), k, 1, 4) + m1*m2*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4) + k1*m1*symsum(exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4),                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  k1*m2*symsum((root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T))/(2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 - c1*k2 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m1 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m2 + 4*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3*m1*m2), k, 1, 4),                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 c1*m2*symsum((root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T))/(2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 - c1*k2 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m1 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m2 + 4*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3*m1*m2), k, 1, 4) + k1*m2*symsum(exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4)]
[                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 c1*k2*symsum((root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T))/(2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 - c1*k2 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m1 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m2 + 4*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3*m1*m2), k, 1, 4) - k1*m2*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4) + k1*k2*symsum(exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4), k1*m1*symsum((root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T))/(2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 - c1*k2 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m1 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m2 + 4*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3*m1*m2), k, 1, 4) + c1*m1*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4) + m1*m2*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4),                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                k1*m2*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4),                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              k1*m2*symsum((root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T))/(2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 - c1*k2 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m1 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m2 + 4*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3*m1*m2), k, 1, 4) + c1*m2*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4)]
[                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   k1*m1*symsum((root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T))/(2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 - c1*k2 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m1 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m2 + 4*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3*m1*m2), k, 1, 4) + k2*m1*symsum((root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T))/(2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 - c1*k2 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m1 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m2 + 4*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3*m1*m2), k, 1, 4) + c1*k2*symsum(exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4),                                                                                                                                                                                                       c1*m1*symsum((root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T))/(2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 - c1*k2 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m1 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m2 + 4*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3*m1*m2), k, 1, 4) + k1*m1*symsum(exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4) + k2*m1*symsum(exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4), k1*m2*symsum((root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T))/(2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 - c1*k2 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m1 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m2 + 4*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3*m1*m2), k, 1, 4) + c1*m1*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4) + c1*m2*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4) + m1*m2*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4) - c1*k2*symsum(exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4),                                                                                                    c1*m2*symsum((root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T))/(2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 - c1*k2 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m1 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m2 + 4*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3*m1*m2), k, 1, 4) + m1*m2*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4) + k1*m2*symsum(exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4)]
[                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              c1*k2*symsum((root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T))/(2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 - c1*k2 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m1 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m2 + 4*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3*m1*m2), k, 1, 4) + k1*m1*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4) + k2*m1*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4),   k1*m1*symsum((root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T))/(2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 - c1*k2 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m1 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m2 + 4*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3*m1*m2), k, 1, 4) + k2*m1*symsum((root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T))/(2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 - c1*k2 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m1 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m2 + 4*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3*m1*m2), k, 1, 4) + c1*m1*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4),                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      k1*k2*symsum(exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4) - k1*m1*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4), k1*m2*symsum((root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T))/(2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 - c1*k2 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m1 + 3*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2*c1*m2 + 4*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3*m1*m2), k, 1, 4) + c1*m2*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4) + m1*m2*symsum((exp(root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*T)*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3)/(3*c1*m1*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 - c1*k2 + 3*c1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^2 + 4*m1*m2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)^3 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m1 + 2*root(m1*m2*s3^4 + c1*m2*s3^3 + c1*m1*s3^3 + k1*m2*s3^2 + k1*m1*s3^2 - c1*k2*s3 - k1*k2, s3, k)*k1*m2), k, 1, 4)]

//实验1：
subs(res,{k1,k2,c1,m1,m2,T},{83000,230000,2950,374,50,0.016666666})
 
ans =//结果太复杂，需要查matlab的syssum，root的意义！
 
[ 1250800*symsum((exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 18700*symsum((exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 31042000*symsum((root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)*exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744))/(70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) + 3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 - 678500000), k, 1, 4),                                                                                                 31042000*symsum(exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 18700*symsum((exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 1103300*symsum((root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)*exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744))/(70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) + 3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 - 678500000), k, 1, 4),                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          4150000*symsum((root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)*exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744))/(70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) + 3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 - 678500000), k, 1, 4),                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  4150000*symsum(exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 147500*symsum((root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)*exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744))/(70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) + 3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 - 678500000), k, 1, 4)]
[                                                                                          19090000000*symsum(exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) - 4150000*symsum((exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 678500000*symsum((root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)*exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744))/(70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) + 3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 - 678500000), k, 1, 4), 1103300*symsum((exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 18700*symsum((exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 31042000*symsum((root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)*exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744))/(70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) + 3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 - 678500000), k, 1, 4),                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        4150000*symsum((exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4),                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  147500*symsum((exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 4150000*symsum((root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)*exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744))/(70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) + 3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 - 678500000), k, 1, 4)]
[                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               678500000*symsum(exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 117062000*symsum((root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)*exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744))/(70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) + 3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 - 678500000), k, 1, 4),                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 117062000*symsum(exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 1103300*symsum((root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)*exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744))/(70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) + 3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 - 678500000), k, 1, 4), 1250800*symsum((exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) - 678500000*symsum(exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 18700*symsum((exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 4150000*symsum((root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)*exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744))/(70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) + 3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 - 678500000), k, 1, 4),                                                                                                 4150000*symsum(exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 18700*symsum((exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 147500*symsum((root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)*exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744))/(70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) + 3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 - 678500000), k, 1, 4)]
[                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               117062000*symsum((exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 678500000*symsum((root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)*exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744))/(70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) + 3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 - 678500000), k, 1, 4),                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 1103300*symsum((exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 117062000*symsum((root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)*exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744))/(70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) + 3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 - 678500000), k, 1, 4),                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                19090000000*symsum(exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) - 31042000*symsum((exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4), 147500*symsum((exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 18700*symsum((exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744)*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3)/(3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 + 70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) - 678500000), k, 1, 4) + 4150000*symsum((root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)*exp((4803839410374945*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k))/288230376151711744))/(70384000*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k) + 3752400*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^2 + 74800*root(s3^4 + (12508*s3^3)/187 + (351920*s3^2)/187 - (6785000*s3)/187 - 190900000/187, s3, k)^3 - 678500000), k, 1, 4)]

 

缺点：最后给出的结果含有级数，不便于编程实现！

 

2）使用c2d函数：

//直接给定数值数组A:
k1=83000;
k2=230000;
c1=2950;
m1=374;
m2=50;

A=[0 1 0 0;-k1/m1 -c1/m1 k1/m1 c1/m1;0 0 0 1;(k1+k2)/m2 c1/m2 -k1/m2 -c1/m2]
B=[0;0;0;-k2/m2]
//用c2d离散化：
T=0.005555555;
[G,H]=c2d(A,B,T)