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Because choice of coordinate system is arbitrary when solving physical systems (or anything for that matter), choosing generalized coordinates is the practice of using the simplest possible coordinate system available for your problem, because even though your chosen coordinates might be silly and useless in practice, they result in the cleanest equations.

Is this in any way correct? And if I'm totally off base could someone help me or point to where I can be helped? I've found a lot of pages which mathematically explain them to me but nowhere has yet done a good job of explaining why.