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Mathematical Modeling of a Roller Coaster
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     Let us assume that we would like to design a roller
coaster. Here are three of the issues we need to deal
with: Is our model three-dimensional or two-dimensional?
Do we know how to account for parameters such as
acceleration, friction, profile of the track, etc.? Can we
express the physics of the problem in mathematical
terms?
     Depending on how sophisticated and realistic you
would like the analysis to be, the physics of roller coasters
can be modeled and studied. We are showing here a
couple of simple examples just to illustrate the point. In
the following example we define the track as a table and
set up the model for making various calculations and
seeing the results graphically.
     The mathematical model was set up using TK Solver.
Once the mathematics was known it took just a few
minutes of work to create the TK Solver model.
Inputs to the first model are shown below.
Outputs are the plots.

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