PROBLEM 9.181 CONTINUED Solving yields 123190.363383 1.7199512ζζζ===The principal moments of inertia are then 210.363Kma=W221.583a=W231.720a=W(b) To determine the direction cosines , xyzλλλof each principal axis, we use two of the equations of Equations (9.54) and Equation (9.57). Thus ( )0xxxyyzxzIKIIλλλ−−−=(9.54a) ( )0zx xyz yzzIIIK−−+−=(9.54c) 2221xyz++=(9.57) Note: Since ,xyyzII=Equations (9.54a) and (9.54c) were chosen to simplify the “elimination” of yduring the solution process. Substituting for the moments and products of inertia in Equations (9.54a) and (9.54c) 22213110122xyzmaKmama−−−−=211130212zmamamaK
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