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274_Problem CHAPTER 9

# 274_Problem CHAPTER 9 - PROBLEM 9.184 CONTINUED(b To...

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PROBLEM 9.184 CONTINUED ( b ) To determine the direction cosines , x yz λ λλ of each principal axis, use two of the equations of Equations (9.54) and (9.57). Then 1 : K Begin with Equations (9.54a) and (9.54b). () ( ) ( ) ( ) 1 1 1 1 0 xx x y y z x z IK I I λλλ −−= ( ) ( )( ) ( ) 2 1 1 1 0 xy x y y yz z II K I −+ = Substituting 22 2 1 1 1 11 3 0.163917 0 24 8 xyz WW W aa a gg g   −− =     2 1 1 1 1 0.163917 0 48 xy z W a g = Simplifying yields ( ) ( ) ( ) 1 1 1 1.34433 1.5 0 z −= ( ) ( ) ( ) 1 1 1 0.299013 0.149507 0 z = Adding and solving for ( ) 1 z ( ) ( ) 1 1 0.633715 zx = and then ( ) ( ) ( ) 1 1 1.34433 1.5 0.633715 yx =− ( ) 1 0.393758 x = Now substitute into Equation (9.57) () () () 2 1 0.393758 0.633715 1 x + += or ( )
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