remember when physicists were able to solve problems with closed-form solutions. lol
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Classical physics can deliver a closed form solution to the 2-body problem. Lifetimes have been spent trying to generalize that to 3. The classic 3-body problem is the Moon's orbit with respect to the Earth and the Sun. This looks like a good summary: http://sites.apam.columbia.edu/courses/ap1601y/Moon-Earth-Sin%20RMP.70.589.pdf …
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I just reviewed the ToC of that article and skimmed through it, but it looks good. Physics is full of perturbative methods and approximations and idealizations that only kinda work in limited contexts.
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Breaking everything down in linear approximations is a good starting point. How do you eat an elephant? One bite at a time. Apply superposition, assume the whole is the sum of the parts, and each part can be considered in isolation. Works for a wide range of problems.
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There's a wider range of problems that go non-linear where things begin to get tricky and eventually cannot be solved at all except in a qualitative sense with heuristics and general guidelines.
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