Transformation Law

1 min read Updated Fri Apr 24 2026 10:11:15 GMT+0000 (Coordinated Universal Time)

The 2 sets of axes must share the origin.

{" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} Ix1x1=Ixx+Iyy2+(IxxIyy2)cos2θIxysin2θI_{x_1x_1} = \frac{I_{xx} + I_{yy}}{2} + \bigg(\frac{I_{xx} - I_{yy}}{2}\bigg)\cos{2\theta} - I_{xy}\sin{2\theta} Iy1y1=Ixx+Iyy2(IxxIyy2)cos2θ+Ixysin2θI_{y_1y_1} = \frac{I_{xx} + I_{yy}}{2} - \bigg(\frac{I_{xx} - I_{yy}}{2}\bigg)\cos{2\theta} + I_{xy}\sin{2\theta} Ix1y1=(IxxIyy2)sin2θ+Ixycos2θI_{x_1y_1} = \bigg(\frac{I_{xx} - I_{yy}}{2}\bigg)\sin{2\theta} + I_{xy}\cos{2\theta}