In work on floating bodies he demonstrated that the orientation of a floating objects is the one that makes its center of gravity as low as possible. He developed mathematical techniques for finding the centers of gravity of objects of uniform density of various well-defined shapes, in particular a triangle, a hemisphere, and a frustum of a circular parabolic.
The center of gravity is an important point on an aircraft, as it defines the amount of mass forward or behind the center of gravity that needs to be moved in order to pitch the plane up or down without applying any external forces. In conventional designs the Co G is often located very near the line 1/3rd back from the front of the wing. That is the line where most wings generate their lift, known as the center of pressure (Co P), so by balancing the plane at that point, the lift and weight balance out with no net torque. The Co is sometimes moved slightly to the rear of this line in order to provide the plane with a natural "nose up" tendency when lift increases (like when applying more power).
If the balance of the plane is moved too far from the Cog, the control surfaces may have trouble controlling the plane. The actual force generated by the surfaces is typically quite small (a few pounds) but due to their location at the end of the tail (typically) they generate considerable torque to pitch the plane. If the Co starts to move away from the Co P there will be an increasing amount of constant torque they have to counteract, and if it moves too far, it may be more than the controls can counter.
The center of gravity is a geometric property of any object. The center of gravity is the average location of the weight of an object. We can completely describe the motion of any object through space in terms of the translation of the center of gravity of the object from one place to another and the rotation of the