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 Oxy, 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 Oxy, and A1,B1 and H1 are the moments of inertia with respect to Ox1y1.
In Chapter 5, we studied the rotation of rigid bodies about an axis of symmetry. For these cases, we have L=Iω, where I is the moment of inertia with respect to t...In Chapter 5, we studied the rotation of rigid bodies about an axis of symmetry. For these cases, we have L=Iω, where I is the moment of inertia with respect to the rotation axis. In this section, we’ll derive the more general form, in which the number I is replaced by a 2-tensor, i.e., a map from a vector space (here R3) into itself, represented by a 3×3 matrix.
The inertia tensor is a real symmetric matrix. A property of real symmetric matrices is that there exists an orientation of the coordinate frame, with its origin at the chosen body-fixed point O , su...The inertia tensor is a real symmetric matrix. A property of real symmetric matrices is that there exists an orientation of the coordinate frame, with its origin at the chosen body-fixed point O , such that the inertia tensor is diagonal. The coordinate system for which the inertia tensor is diagonal is called the Principal axis system which has three perpendicular principal axes.
