Roller Coaster Reconstruction

Oliver Knill, Summer 2019 to Summer 21

Content in a Mathematica file is organized as cells. To evaluate a cell, grab the bracket to the right, holding down the <shift> key and hit return.

Reconstructing a curve from acceleration data

In the following lines we first define a curve r(t), then compute a list A of acceleration data. From that by summation we produce the velocity data V and then the position data W. Please run the following code by clicking into the green cell, then  holding down the <shift> key and hitting return. If you have trouble with getting started, please talk to each other.

r[t_]:={Cos[t],Cos[5 t],Cos[3 t]};
ParametricPlot3D[r[t]-r[0],{t,0,2 Pi}]

Reconstruction from real data

Now we load the data collected from a smartphone as described in the last part of HW 5

Import["rollercoaster.m"];

You can see the cata by removing the semicolon from the previous line and running the cell again again by hitting return while holding down the <shift> key. Now, we reconstruct the curve as before. This can take a while but you will see a curve.

M=Length[A];dt=1/M;
V=Table[Sum[A[[j]] dt,{j,k}],{k,M}];
P=Table[Sum[V[[j]] dt,{j,k}],{k,M}];
Graphics3D[{Red,Map[Point,P]},AspectRatio->1]