Principale Momenten van Oppervlakte

The moments and product of inertia of an area about inclined axes can be calculated using the coordinate transformation relations.

A set of axes corresponding to the maximum and minimum moments of inertia is called the principal axes.

Differentiating either moment of inertia about the inclined axis with respect to the inclination angle and equating the result to zero gives the orientation of the principal axes.

The roots of the resulting equation define two angles ninety degrees apart, specifying the orientation angle of the major and minor principal axes.

The moments of inertia about the inclined axes are rewritten by substituting the sine and cosine terms. The expression is further simplified to obtain the principal moments of inertia.

At these angles, the product of inertia is zero.

If an area possesses an axis of symmetry, then axis of symmetry is the principal axis. In contrast, the principal axes need not be the symmetric axis.

If the origin coincides with the centroid, the principal axes denote the principal centroidal axes.