How to Have Smaller Intervals in TimeSeries

Question

I have a wolfram demonstration project with the following code:

Manipulate[
 
 dist = 5;
 
 posA = -dist;
 posB = dist;
 vA2 = -((-mA vA1 + ee mB vA1 - mB vB1 - ee mB vB1)/(mA + mB));
 vB2 = -((-mA vA1 - ee mA vA1 + ee mA vB1 - mB vB1)/(mA + mB));
 
 (* vA1*t-dist+mA/10=vB1*t+dist+mB/10, (vA1-vB1)*t=2*dist+mB/10 *)
 tImpact = (20 dist - mA - mB)/(10 (vA1 - vB1));
 
 posImpactA = posA + vA1 tImpact;
 posImpactB = posB + vB1 tImpact;
 c1 = (vA2 - vA1)/2 Tanh[ (10 x)/dt - (10 tImpact)/dt] + (vA2 + vA1)/2;
 c2 = (vB2 - vB1)/2 Tanh[(10 x)/dt - (10 tImpact)/dt] + (vB1 + vB2)/2;
 
 posA2 = If[tt <= tImpact, vA1 tt + posA, 
   posImpactA + vA2*(tt - tImpact)];
 posB2 = If[tt <= tImpact, vB1 tt + posB, 
   posImpactB + vB2*(tt - tImpact)];
 
 vecB = If[
   tt <= tImpact,
   {Red, Thick, Arrow[{{posB2, 0}, {posB2 + vB1, 0}}]},
   {Darker[Green], Thick, Arrow[{{posB2, 0}, {posB2 + vB2, 0}}]}
   ];
 vecA = If[
   tt <= tImpact,
   {Red, Thick, Arrow[{{posA2, 0}, {posA2 + vA1, 0}}]},
   {Darker[Green], Thick, Arrow[{{posA2, 0}, {posA2 + vA2, 0}}]}
   ];
 If[sh,
  Show[
   Plot[Tooltip[{vA1, vB1}], {tt, 0, tImpact - dt/2}, 
    PlotRange -> {{0, 5}, {-10, 10}}, 
    PlotStyle -> {{AbsoluteThickness[3]}, {AbsoluteThickness[3]}}, 
    PlotLabel -> "velocity versus time", 
    AxesLabel -> {t , Subscript[v, x]}],
   Plot[Tooltip[{vA2, vB2}], {tt, tImpact + dt/2, 5}, 
    PlotStyle -> {{AbsoluteThickness[3]}, {AbsoluteThickness[3]}}],
   Plot[{c1, c2}, {x, tImpact - dt/2, tImpact + dt/2}, 
    PlotStyle -> {{AbsoluteThickness[3]}, {AbsoluteThickness[3]}}],
   ImageSize -> {550, 275}], 
  timeSeries = 
   Table[{vA1, vB1, vA2, vB2, tt}, {tt, 0.1, tImpact + dt/2, 5}], 
  Graphics[{
    (* road *) {Lighter[Gray], Arrow[{{-10, 0}, {10, 0}}]},
    (* disk for A *) {RGBColor[0.368417, 0.506779, 0.709798], 
     EdgeForm[Black], Disk[{posA2, 0}, mA/10]},
    (* disk for B *) {RGBColor[0.880722, 0.611041, 0.142051], 
     EdgeForm[Black], Disk[{posB2, 0}, mB/10]}, vecA, vecB}, 
   PlotRange -> {{-10, 10}, {-6.6, 6.6}}, ImageSize -> {550, 275}]
  ],
 Grid[{
   {
    Spacer[40],
    Control[{{mA, 1, "mass of A"}, 1, 10, 0.1, 
      Appearance -> "Labeled", ImageSize -> Small}], 
    Control[{{vA1, 5, "initial velocity of A"}, 1, 5, 0.1, 
      Appearance -> "Labeled", ImageSize -> Small}]
    },
   {
    Spacer[40],
    Control[{{mB, 10, "mass of B"}, 1, 10, 0.1, 
      Appearance -> "Labeled", ImageSize -> Small}], 
    Control[{{vB1, 0, "initial velocity of B"}, -5, 0, 
      Appearance -> "Labeled", ImageSize -> Small}]
    },
   {
    Spacer[40],
    Control[{{tt, 0, "time"}, 0, 5, 0.1, Appearance -> "Labeled", 
      ImageSize -> Small}], 
    Control[{{ee, 1, "coefficient of elasticity"}, 0, 1, 0.1, 
      Appearance -> "Labeled", ImageSize -> Small}]
    },
   {
    Spacer[40],
    Control[{{sh, False, "velocity plot"}, {True, False}, 
      ImageSize -> Small}], 
    Control[{{dt, 0.1, "collision time"}, 0.01, 1.5, 
      Appearance -> "Labeled", ImageSize -> Small}]
    }
   },
  Alignment -> Left],
 TrackedSymbols -> True,
 AutorunSequencing -> {1, 2, 3, 4, 6, 7}]
Export["file.txt", timeSeries, "Table"]

I modified it so that I can get a Table of the initial and final velocities of both masses over time using the timeSeries and Table function. The problem is when I open the file I get:

5   0   -45/11  10/11   1.83
5   0   -45/11  10/11   2.83
5   0   -45/11  10/11   3.83
5   0   -45/11  10/11   4.83

How can I modify it so that I can get the velocities at smaller time intervals, for example 0.1 seconds instead of 1 second as shown in the table that I generated.

EDIT

I am as can be seen from the graph generated from the demonstration trying to find the velocities when it changes during the collision:

Thank you.

*EDIT Based on the answer below I get a table that looks like:

7/4 {4.977521607666957, 0.0022478392333043495}
351/200 {4.93915590068832, 0.006084409931168044}
44/25   {4.836489000344622, 0.016351099965537796}
353/200 {4.5688556983857564, 0.043114430161424355}
177/100 {3.916337072526204, 0.10836629274737963}
71/40   {2.555077987545499, 0.24449220124545012}
89/50   {0.45454545454545453, 0.45454545454545453}
357/200 {-1.6459870784545898, 0.6645987078454589}
179/100 {-3.007246163435295, 0.8007246163435294}
359/200 {-3.6597647892948477, 0.8659764789294847}
9/5 {-3.9273980912537136, 0.8927398091253713}
361/200 {-4.030064991597412, 0.9030064991597411}
181/100 {-4.068430698576049, 0.9068430698576047}
363/200 {-4.082626807323631, 0.908262680732363}
91/50   {-4.087860453359396, 0.9087860453359395}
73/40   {-4.089787322036489, 0.9089787322036489}

Are the terms in the brackets the final velocities of the mass A and mass B and outside the brackets is the time? How can I insert the initial velocities as well? Also, how can I get rid of the brackets so that I can use this data automatically.

Answer 1

I inserted some code, that will calculate 100 time steps between t=0..5. The output is available outside the Manipulate in variable velocities. It corresponds to the current setting. If you want more resolution, feel free to change the time step in the Table command.

The first number in a row is the time, The next two, the initial and the last to the final velocities.

Here is the inserted code

....

vecA = If[
   tt <= tImpact, {Red, Thick, 
    Arrow[{{posA2, 0}, {posA2 + vA1, 0}}]}, {Darker[Green], Thick, 
    Arrow[{{posA2, 0}, {posA2 + vA2, 0}}]}];

vel[t_] = Piecewise[{
    {{vA1, vB1}, 0 <= t < tImpact - dt/2},
    {{c1, c2} /. x -> t, tImpact - dt/2 <= t < tImpact + dt/2},
    {{vA2, vB2}, tImpact - dt/2 <= t <= 5},
    {0, True}
    }];
velocities = 
  Table[{t, vA1, vB1, Sequence @@ vel[t]}//N, {t, 0, 5, 5/100}];    


If[sh, Show[Plot[Tooltip[{vA1, vB1}], {tt, 0, tImpact - dt/2},

....