Semester 1 / Mechanics / Statics / Transformation Law

Transformation Law

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The 2 sets of axes must share the origin.

{" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} {" "} Ix1x1=Ixx+Iyy2+(Ixx−Iyy2)cos⁡2θ−Ixysin⁡2θI_{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−(Ixx−Iyy2)cos⁡2θ+Ixysin⁡2θI_{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=(Ixx−Iyy2)sin⁡2θ+Ixycos⁡2θI_{x_1y_1} = \bigg(\frac{I_{xx} - I_{yy}}{2}\bigg)\sin{2\theta} + I_{xy}\cos{2\theta}
Written by September 29, 2026 1 min read
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