I'm studying classical mechanics, but without those stuffs Lagrangians and Hamiltonian mechanics...just Newtonian..the problem is a find hard to learn this non-inertial frames system, like $r=R+r'$...only that I find difficuly, because they say "the absolute vector is the sum of the distance between the origins and the relative vector of the rotating system", but how can I add two vector of different basis systems? How can I say after I add these two vectors of different basis axis, and say that the result, belongs necessarily to the first basis system? Can anyone tell me about a book that goes deep into this with a good amount of graphics and examples?
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