# Wolfram 语言™

## 建立一个吊链模型

In[1]:=
`L = 4; a = 1; b = 3; `

In[2]:=
`xf = 1; nh = 201; h := xf/nh;`

In[3]:=
`varsy = Array[y, nh + 1, {0, nh}];`

In[4]:=
`varsm = Array[m, nh + 1, {0, nh}];`

In[5]:=
`varsv = Array[v, nh + 1, {0, nh}];`

In[6]:=
`varss = Array[s, nh + 1, {0, nh}];`

In[7]:=
`vars = Join[varsm, varsy, varsv, varss];`

In[8]:=
`objfn = v[nh];`

In[9]:=
`bndcons = {y[0] == a, y[nh] == b, v[0] == 0, s[0] == 0, s[nh] == L};`

In[10]:=
```odecons = {Table[ y[j + 1] == y[j] + 0.5*h*(m[j] + m[j + 1]), {j, 0, nh - 1}], Table[v[j + 1] == v[j] + 0.5* h*(y[j]*Sqrt[1 + m[j]^2] + y[j + 1]*Sqrt[1 + m[j + 1]^2]), {j, 0, nh - 1}], Table[s[j + 1] == s[j] + 0.5*h*(Sqrt[1 + m[j]^2] + Sqrt[1 + m[j + 1]^2]), {j, 0, nh - 1}]};```

In[11]:=
```tmin = If[b > a, 0.25 , 0.75]; init = Join[Table[4*Abs[b - a]*((k/nh) - tmin), {k, 0, nh}], Table[4*Abs[b - a]*(k/nh)*(0.5*(k/nh) - tmin) + a, {k, 0, nh}], Table[(4*Abs[b - a]*(k/nh)*(0.5*(k/nh) - tmin) + a)*4* Abs[b - a]*((k/nh) - tmin), {k, 0, nh}], Table[4*Abs[b - a]*((k/nh) - tmin), {k, 0, nh}]];```

In[12]:=
```sol = FindMinimum[{objfn, Join[bndcons, odecons]}, Thread[{vars, init}]];```

In[13]:=
`solpts = Table[{i h, y[i] /. sol[[2]]}, {i, 0, nh}];`

In[14]:=
`ListPlot[solpts, ImageSize -> Medium, PlotTheme -> "Marketing"]`
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FindFit 将结果与悬链曲线拟合.

In[15]:=
`catenary[t_] = c1 + (1/c2) Cosh[c2 (t - c3)];`
In[16]:=
`fitsol = FindFit[solpts, catenary[t], {c1, c2, c3}, {t}]`
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In[17]:=
```Show[Plot[catenary[t] /. fitsol, {t, 0, 1}, PlotStyle -> Directive[Green, Thickness[0.01]], ImageSize -> Medium], ListPlot[Take[solpts, 1 ;; nh ;; 5], PlotStyle -> PointSize[.02]]] ```
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