Skip to main content

differential equations - Derivative of function solved from NDSolve can't be plotted


I have used NDSolve to solve for a function (an angle of a triple pendulum), and now I wish to plot the derivative of that function (the angular velocity). Mathematica plots an empty plot. I had this issue before with a double pendulum system and ended up having to copy and paste cells into a new notebook one by one, and reevaluating everything. Then it suddenly started working (for the double pendulum). Doing that is not working in the case of my triple pendulum; the plot is still empty.


Needs["VariationalMethods`"]

ClearAll[Global]

variables = {Subscript[θ, 1][t], Subscript[θ, 2][t], Subscript[θ, 3][t]};
Subscript[r, 1] = 
  Subscript[l, 1] {Sin[Subscript[θ, 1][t]], -Cos[Subscript[θ, 1][t]]};
Subscript[r, 2] = Subscript[r, 1] + 
  Subscript[l, 2] {Sin[Subscript[θ, 2][t]], -Cos[Subscript[θ, 2][t]]};
Subscript[r, 3] = Subscript[r, 2] + 
  Subscript[l, 3] {Sin[Subscript[θ, 3][t]], -Cos[Subscript[θ, 3][t]]};


Subscript[l, 1] = 1;
Subscript[l, 2] = 1;
Subscript[l, 3] = 1;
Subscript[m, 1] = 1;
Subscript[m, 2] = 1;
Subscript[m, 3] = 1;
g = 9.81; tMax = 10;
initial = 
  {Subscript[θ, 1][0] == Pi/2, Subscript[θ, 2][0] == Pi, Subscript[θ, 3][0] == Pi/2,
   Subscript[θ, 1]'[0] == Pi/2, Subscript[θ, 2]'[0] == 0, Subscript[θ, 3]'[0] == 0};


lagrangian = (Subscript[m, 1]/2) D[Subscript[r, 1], t].D[Subscript[r, 
      1], t] + (Subscript[m, 2]/2) D[Subscript[r, 2], t].D[Subscript[
      r, 2], t] + (Subscript[m, 3]/2) D[Subscript[r, 3], t].D[
      Subscript[r, 3], t] - g {0, 1}.(Subscript[m, 1]*Subscript[r, 1] + 
       Subscript[m, 2]*Subscript[r, 2] + Subscript[m, 3]*Subscript[r, 3]);
eqs = EulerEquations[lagrangian, variables, t];

sol = First[NDSolve[Join[eqs, initial], variables, {t, 0, tMax}]];
Plot[Subscript[θ, 2]'[t] /. sol, {t, 0, 10}]


and the plot is blank. Like I said, I did the exact same code for the double pendulum, except the Lagrangian was slightly different (no third mass), and I was working with fewer variables. I had the same problem; there was no plot. After copying and pasting, it started working. But no amount of copying and pasting and renaming variables is working with the triple pendulum.


Notice Subscript[θ, 2][t] /. sol /. t -> 5 gives an answer of -5.75151. But notice Subscript[θ, 2]'[t] /. sol /. t -> 5 simply spits out Derivative[1][Subscript[θ, 2]][5] (the same thing). So the derivative has not been calculated at all, it seems.


Why is there no plot?


Note: the theta function plots fine. I'm wanting to plot the derivative of each theta function. That is not working.




Comments

Post a Comment

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

plotting - Magnifying Glass on a Plot

Although there is a trick in TEX magnifying glass but I want to know is there any function to magnifying glass on a plot with Mathematica ? For example for a function as Sin[x] and at x=Pi/6 Below, this is just a picture desired from the cited site. the image got huge unfortunately I don't know how can I change the size of an image here! Answer Insetting a magnified part of the original Plot A) by adding a new Plot of the specified range xPos = Pi/6; range = 0.2; f = Sin; xyMinMax = {{xPos - range, xPos + range}, {f[xPos] - range*GoldenRatio^-1, f[xPos] + range*GoldenRatio^-1}}; Plot[f[x], {x, 0, 5}, Epilog -> {Transparent, EdgeForm[Thick], Rectangle[Sequence @@ Transpose[xyMinMax]], Inset[Plot[f[x], {x, xPos - range, xPos + range}, Frame -> True, Axes -> False, PlotRange -> xyMinMax, ImageSize -> 270], {4., 0.5}]}, ImageSize -> 700] B) by adding a new Plot within a Circle mf = RegionMember[Disk[{xPos, f[xPos]}, {range, range/GoldenRatio}]] Show...
Post a Comment
Read more