Joe Shearer
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Center of gravity is center of gravity, you can shift it by design... but than you have new center of gravity!
Perhaps you meant its not intentionally kept at middle of the structure!
Yes, you are right, it is intentionally not kept in the middle of the structure.
Let me try a more relaxed wording: a plane may be designed, originally, with a centre of gravity located so that it is aerodynamically stable. In order to make it more manoeuvreable, we may then shift the centre of gravity further back, by, for instance, increasing the weight of the rear section by a few kgs. With this modification, the aircraft is now dynamically unstable.