Problem #6 Integrate the tensor of position vectors y; over the surface of a cube, where...

Transcribed Image Text:

Problem #6 Integrate the tensor of position vectors y; over the surface of a cube, where y; points from the origin to any point on the surface of the cube. The coordinate axes of the cube are centered in the boundary and are normal to the axes. Find a simplified expression for Iij. Hint 1: There is no preferred direction for a cube, so the answer will take an isotropic form. Hint 2: You might want to consider the component In (or 122 or I33) in solving the problem. Keep in mind that y, is not a surface normal, so you will need to consider all 6 faces of the cube. Iij = y; dA (4) 2R X2 x3 Problem #6 Integrate the tensor of position vectors y; over the surface of a cube, where y; points from the origin to any point on the surface of the cube. The coordinate axes of the cube are centered in the boundary and are normal to the axes. Find a simplified expression for Iij. Hint 1: There is no preferred direction for a cube, so the answer will take an isotropic form. Hint 2: You might want to consider the component In (or 122 or I33) in solving the problem. Keep in mind that y, is not a surface normal, so you will need to consider all 6 faces of the cube. Iij = y; dA (4) 2R X2 x3