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282_Problem CHAPTER 9 - PROBLEM 9.186 CONTINUED y)1 = z)1 =...

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PROBLEM 9.186 CONTINUED ( ) ( ) ( ) 1 1 1 0.49965 y z x λ λ λ = = ( ) ( ) 1 2 2 1 2 0.49965 1 x x λ λ + = ( ) 1 0.81669 x λ = ( ) ( ) 1 1 0.40806 y z λ λ = = ( ) 1 35.2 ; x θ = ° ( ) ( ) 1 1 65.9 y z θ θ = = ° W K 2 : Begin with Equations (9.54a) and (9.54b): ( )( ) 2 2 2 2 ( ) ( ) 0 x x xy y zx z I K I I λ λ λ = ( ) ( )( ) ( ) 2 2 2 2 0 xy x y y yz z I I K I λ λ λ + = Substituting: ( ) ( ) 3 3 3 2 2 2 14.32 10 18.62 10 4.297 10 ( ) ( ) 0 x y z λ λ λ × × × = (i) ( ) ( ) ( ) 3 3 3 2 2 4.297 10 18.62 10 18.62 10 0 x y λ λ × + × × = (ii) From (ii) ( ) 2 0 x λ = From (i) ( ) ( ) 2 2 y z λ λ = − Substituting: ( ) ( ) ( ) 2 2 2 2 2 2 1 x y z λ λ λ + + = ( ) 2 1 2 y λ = ( ) ( ) ( ) 2 2 2 90.0 , 45.0 , 135.0 x y z θ θ θ = ° = ° = ° W K 3 : Begin with Equations (9.54b) and (9.54c) ( ) ( )( ) ( ) 3 3 3 3 0 xy x y y yz z I I K I λ λ λ + + = ( ) ( ) ( ) ( ) 3 3 3 0 zx x yz y z z I I I K λ λ λ + = Substituting: ( ) ( ) ( ) 3 3 3 3 3 4.297 10 18.62
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