268_Problem CHAPTER 9

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 and z 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 II = = , we have ( )( ) ( ) 1 1 1 0 xx x y y IK I −= λλ ( ) ( )( ) 1 1 1 0 xy x y y K +− = Substituting ( ) () ( ) 33 3 1 1 34.106 10 34.876 10 0.96211 10 0 xy −− × −× × = ( )( ) 3 1 1 0.96211 10 50.125 10 34.876 10 0 ×+ × × = or ( ) ( ) 1 1 0.770 10 0.96211 10 0 ×− ×= ( ) ( ) 1 1 0.96211 10 15.249 10 0 Solving yields ( ) ( ) 1 0 == From Equation 9.57 () () () () 2 22 11 1 1 1 or 1 xyz z + += = λλλ and ( ) ( ) ( ) 1 1 1 90.0 ,
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This note was uploaded on 07/11/2011 for the course EGM 2511 taught by Professor Jenkins during the Spring '08 term at University of Florida.

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