If, in the previous problem, the coordinate axes are rotated through and angle θ about the x3-axis, show that the new inertia tensor is




And hence show that the x1- and x2-axes become principal axes if the angle of rotation is θ = ½tan€“1 (2C/B €“ A)

A' -C {I} -C' B' O A' + B' where A' = A cos 0- C sin 20 + B sin2 0 B' = A sin? 0 + C sin 20 + B cos? 0 C' = C cos 2e (B - A) sin 20