264_Problem CHAPTER 9

264_Problem CHAPTER 9 - PROBLEM 9.181 CONTINUED Solving...

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PROBLEM 9.181 CONTINUED Solving yields 12 3 19 0.363383 1.71995 12 ζζ ζ == = The principal moments of inertia are then 2 1 0.363 Km a = W 2 2 1.583 a = W 2 3 1.720 a = W ( b ) To determine the direction cosines , x yz λ λλ of each principal axis, we use two of the equations of Equations (9.54) and Equation (9.57). Thus ( ) 0 xx x y y z x z IK I I λλλ −−= (9.54a) ( ) 0 zx x yz y z z II I K −+ = (9.54c) 222 1 xyz + += (9.57) Note: Since , x yy z I I = Equations (9.54a) and (9.54c) were chosen to simplify the “elimination” of y during the solution process. Substituting for the moments and products of inertia in Equations (9.54a) and (9.54c) 22 2 13 1 1 0 12 2 xy z ma K ma ma  −− =   2 11 1 3 0 21 2 z ma ma ma K
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