y y' m M a X а m M X' Inertia tensor for 4 point masses Description of the sketch: Two different masses at the corner
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y y' m M a X а m M X'
Inertia tensor for 4 point masses Description of the sketch: Two different masses at the corner of the square: M and m. The lenght of 1 side is 2a Two coordinate systems: x-y and x'-y' (the z and z'-axis are identical and pointing to the observer) The sololution for to the Inertia tensor for I and I' are given : 2(M + m)a -2(M - m)a? 0 I -2(M - ma? 2(M + m)a? 0 0 0 4(M + m)a?) 4Ma2 0 0 1 = 0 4ma? 0 0 0 4(M + m)a? Exercise: 1) Diagonalize the matrix of the inertia tensor I and calculate the transition matrix T: I +1' 2) What meaning does Eigenvalue and transition matrix T has here in a physical context)?