I am looking to study elementary mechanics (physics) from the point of view of differential forms on manifolds, and moments, and am wondering if there are any texts that generalize the notions of moments of inertia, momentum, etc, as well as circular motion to curvilinear coordinates (with examples of how we obtain torque, etc from generalized definitions). From what I have seen, many of these derivations require such mathematics, but I cannot seem to find rigorous, but simplified derivations. Your help would be greatly appreciated. Thank you!
Try the following books.