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    • 3.6: Rotation of Axes, Two Dimensions
      https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Celestial_Mechanics_(Tatum)/03%3A_Plane_and_Spherical_Trigonometry/3.06%3A_Rotation_of_Axes_Two_Dimensions
      We see that \(\text{OA} = x, \ \text{AP} = y, \ \text{ON} = x^\prime, \ \text{PN} = y^\prime, \ \text{OM} = x \cos θ, \ \text{MN} = y \sin θ\), \[\pmatrix{x^\prime \\ y^\prime} = \pmatrix{\cos θ & \si...We see that \(\text{OA} = x, \ \text{AP} = y, \ \text{ON} = x^\prime, \ \text{PN} = y^\prime, \ \text{OM} = x \cos θ, \ \text{MN} = y \sin θ\), \[\pmatrix{x^\prime \\ y^\prime} = \pmatrix{\cos θ & \sin θ \\ -\sin θ & \cos θ} \pmatrix{x \\ y}. \label{3.6.3} \tag{3.6.3}\] \[\pmatrix{x \\ y} = \pmatrix{\cos θ & \sin θ \\ - \sin θ & \cos θ}^{-1} \pmatrix{x^\prime \\ y^\prime} = \pmatrix{\cos θ & -\sin θ \\ \sin θ & \cos θ} \pmatrix{x^\prime \\ y^\prime}. \label{3.6.4} \tag{3.6.4}\]
    • 2.12: Rotation of Axes
      https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Classical_Mechanics_(Tatum)/02%3A_Moments_of_Inertia/2.12%3A_Rotation_of_Axes
      Let us suppose that the axes are in the plane of the lamina and that O is the centre of mass of the lamina. \(A, B \) and \(H\) are the moments of inertia with respect to the axes O\(xy \), and \(A_{1...Let us suppose that the axes are in the plane of the lamina and that O is the centre of mass of the lamina. \(A, B \) and \(H\) are the moments of inertia with respect to the axes O\(xy \), and \(A_{1} , B_{1} \) and \(H_{1} \) are the moments of inertia with respect to O\(x_{1}y_{1} \).

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