Principal Axes:
By now it is clear that the second moment of area and product of area depend on the chosen reference. At any point, there are two axes orthogonal to each other having extreme values for the second moment of area. One of these axes correspond to maximum second moment of area, the other corresponds to minimum second moment of area. These axes are called the principal axes.
To find out the orientation of the principal axes, we have to differentiate Ix'x' with respect q and make the expression equal to zero. Thus,
Second Moments and Products of Area in the rotated Coordinate System |
Thus, Ixx Iyy - Ixy2 is invariant of rotated coordinate axes. This is called the second invariant. |
