Analytical Mech Homework Solutions 121

Analytical Mech Homework Solutions 121 - CHAPTER 9 MOTION...

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CHAPTER 9 MOTION OF RIGID BODIES IN THREE DIMENSIONS 9.1 (a) () 22 xx I yzd m =+ dm dxdy ρ = and ma 2 2 = z ( ) 2 2 00 0 ya x a xx yx I yd x == ∫∫ d y 2a a x = 2 0 2 a ayd y 2 4 2 33 xx ma Ia y ( ) 2 2 yy I xzd m xd x d = y 3 0 8 3 a a dy = 42 84 yy am I a From the perpendicular axis theorem: 2 5 3 zz xx yy ma III =++ 2 xy yx I Ix y d m x y d x = d y 2 0 4 2 a a ydy =− 2 4 2 xy yx ma II a − = 0 xz zx yz zy I z d m I = I (b) 2 5 α = cos , 1 cos 5 β = , cos 0 γ = From equation 9.1.10 … 2 44 1 2 1 2 35 3 5 2 55 ma ma ma I  =+ +   2 2 15 ma = (c) ˆˆ ˆ cos
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