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I never understood newtonian mechanics taught in high school physics until I wrote a simulator for it. The code is generally ~100 lines in python but you really get the feel for how the equations work.

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There is a reason Newtonian Physics was invented and found huge success throughout the 1600s and 1700s. It's such a simple framework that a wide variety of consequences can be obtained by just playing with the equations by hand, even without a calculator. They are just linear first and second order differential equations.

All the questions you asked while writing the code, can be asked to the equations and the consequences worked out almost immediately.

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