3.5: Numerical Applications

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IN THIS SECTION WE APPLY VARIOUS NUMERICAL METHODS to several physics problems after setting them up. We first describe how to work with second order equations, such as the nonlinear pendulum problem. We will see that there is a bit more to numerically solving differential equations than to just running standard routines. As we explore these problems, we will introduce other methods and provide some MATLAB code indicating how one might set up the system.

Other problems covered in these applications are various free fall problems beginning with a falling body from a large distance from the Earth, to flying soccer balls, and falling raindrops. We will also discuss the numerical solution of the two body problem and the Friedmann equation as nonterrestrial applications.