268_Problem CHAPTER 9 - PROBLEM 9.182 CONTINUED(b To...

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PROBLEM 9.182 CONTINUED ( b ) To determine the directions cosines , x y λ λ and z λ of each principal axis use two of the Equations 9.54 and Equation 9.57 1 : K Using Equation 9.54(a) and Equation 9.54(b) with 0 yz zx I I = = , we have ( )( ) ( ) 1 1 1 0 x x xy y I K I = λ λ ( ) ( )( ) 1 1 1 0 xy x y y I I K λ λ + = Substituting ( ) ( ) ( ) 3 3 3 1 1 34.106 10 34.876 10 0.96211 10 0 x y λ λ × × × = ( ) ( ) ( ) 3 3 3 1 1 0.96211 10 50.125 10 34.876 10 0 x y λ λ × + × × = or ( ) ( ) 3 3 1 1 0.770 10 0.96211 10 0 x y λ λ × × = ( ) ( ) 3 3 1 1 0.96211 10 15.249 10 0 x y λ λ × + × = Solving yields ( ) ( ) 1 1 0 x y λ λ = = From Equation 9.57 ( ) ( ) ( ) ( ) 2 2 2 1 1 1 1 1 or 1 x y z z + + = = λ λ λ λ and ( ) ( ) ( ) 1 1 1 90.0 ,
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