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I have an external file in extension XLS with looks as follows:

XLS

This file can be obtained by the link below:

Velocidade Angular

With certainty this file is generating a list inappropriate for the utility that I need, because I cannot use its elements in an appropriate manner.

I have attempted to do a test manually to try to obtain some result as follows:

test={{0, -1.90833*10^-14,0},{0.04, -0.0171878,0},{0.08, -0.0683827, 0},{0.12, -0.153032,0},{0.16, -0.270582, 0},{0.2, -0.42048, 0},{0.24, -0.602173,0}};
time=test[[All,1]];
x=test[[All,2]];

Where $x$ are my displacements in axisX and $time$ the time for each one of them.

  1. This would be my first question: what is wrong with this import?

Getting an answer regarding the first question,

  1. I would like to know if I am proceeding in the best way to obtain a polynomial or a function that describes this movement.

    intf = Interpolation[x, time]

I think that I am doing something wrong, for this cause I am not able to evolve my studies.

Information:

Graphics3D[{Red, Line[data], Black, AbsolutePointSize[6],Point[data]}, BoxRatios -> {3, 2, 1.5}, Axes -> True,ImageSize -> 450]

Using the Graphics3D I can obtain an interesting chart, but my goal is to get something that describes this movement mathematically.

enter image description here

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  • $\begingroup$ Your first entry in `test' list missing a zero (third element). You can do Interpolation[test[[All, 1 ;; 2]]] or Interpolation[Transpose[{time, x}]] $\endgroup$
    – demm
    Commented Jun 24, 2016 at 15:12
  • $\begingroup$ You should then try to fit a model to the data or use FindFormula. $\endgroup$
    – demm
    Commented Jun 24, 2016 at 15:27
  • $\begingroup$ Import[file.xls] always returns a list of sheets, even if there is only one sheet, so you need to do data=First@Import[] or similar. This has to be a duplicate. $\endgroup$
    – george2079
    Commented Jun 24, 2016 at 15:41
  • $\begingroup$ seeing the edit, obviously the exact curve is not going to be polynomial, but trigonometric. What exactly are you trying to accomplish? $\endgroup$
    – george2079
    Commented Jun 24, 2016 at 15:47

1 Answer 1

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Import takes all sheets, which nests the data. First@ takes the first sheet formatting the data you need for the subsequent expressions.

test = First@Import["Velocidade Angular.xls"];

time = test[[All, 1]];
x = test[[All, 2]];

f = Interpolation[Transpose[{time, x}], InterpolationOrder -> 3];

Show[
 ListPlot[test[[All, 1 ;; 2]], PlotStyle -> Red],
 Plot[f[t], {t, time[[1]], time[[-1]]}]
 ]

enter image description here

data = Transpose[{time, x}];

model = a + b t + c t^2 + d t^3;

pos = NonlinearModelFit[data, model, {a, b, c, d}, t]
vel = pos'
acc = pos''

Plot[{pos[t], vel[t], acc[t]}, {t, time[[1]], time[[-1]]}, PlotLegends -> "Expressions"]

pos[t] =-1.0569*^-13 + 9.28177*^-14*t - 10.8*t^2 + 1.44*t^3

vel[t] = 9.28177*10^-14 - 21.6 t +4.32 t^2

acc[t] = -21.6 + 8.64 t

enter image description here

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    $\begingroup$ Since the interpolation is 3rd order the model can be as well. Let me know if the addition above is acceptable. $\endgroup$
    – Young
    Commented Jun 24, 2016 at 15:45
  • $\begingroup$ I added velocity and acceleration to the answer, just in case you have trouble. $\endgroup$
    – Young
    Commented Jun 24, 2016 at 17:01

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