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I am trying to find a project that I can model using differential equations and matlab, that I may also be able to create in the real world and verify my computer models and predictions. This is more for an introductory course, learning for my first time how to use matlab.

I am having difficulty finding ideas, I want something that is interesting, but hasn't been done a million times.

Some examples: modeling hot air balloon lift, modeling and verifying pneumatic gun trajectory and distance, etc.

Most of the ideas I come up with are simple optimization problems, i.e. plug in a value here, and get a value there. I am looking for something more dynamic.

Thanks you very much in advance.