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Analytical Mech Homework Solutions 135

Analytical Mech Homework Solutions 135 - For Problem 9.4 13...

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For Problem 9.4: 2 13 0 0 0 10 0 12 0 0 5 ma I = I , 1 2 14 3 ω ω = G 2 13 0 0 1 0 10 0 2 12 14 0 0 5 3 ma L I ω ω = = G I G 2 13 20 12 14 15 ma ω = ( ) 2 13 1 1 1 2 3 20 2 2 14 12 14 15 ma T L ω ω ω = = G G ( ) ( ) 2 2 2 2 7 13 40 45 24 14 24 ma ma ω ω = + + = 9.22 Since the coordinate axes are axes of symmetry, they are principal axes and all products of inertia are zero. ω G 2c 2b 2a z x From Table 8.3.1, ( ) ( ) ( ) 2 2 2 2 2 2 12 3 xx m m I b c b c = + = + ( ) 2 2 3 yy m I a c = + , ( ) 2 2 3 zz m I a b = + y 2 2 2 2 2 2 0 0 0 0 3 0 0 b c m I a c a b + = + + I ( ) ( ) ( ) 1 2 3 1 2 2 2 2 2 2 2 ˆ ˆ ˆ a ae be ce b a b c a b c c ω ω ω     = + + =   + + + +     G G I G From equation 9.1.28,
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