Analytical Mech Homework Solutions 138

Analytical Mech Homework Solutions 138 - 2 a 3 Thus the...

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2 3 Ha = Thus, the coordinates of the 4 atoms are: Oxygen: () 0,0, H Hydrogen: 11 ,, 0 ; , , 0 22 aa bb  −−   Carbon: 2 ,0,0 b (a) The axes 1, 2, 3 are principal axes if the products of inertia are zero. 00 xy i i i Im x y b b −   −= =+ + +≡     0 00000 yz I − =+++≡ The 1,2,3 axes are principal axes. xz I (b) Find principal moments 2 1 67 16 1 1 6 xx i i i 2 I y zH == + = + + = a () ( ) ( ) 2 2 2 2 21 89 16 1 1 12 6 yy i i i 2 1 2 I x bbb += + + + = a 2 2 2 31 1 14 0 zz i i i 2 2 3 I x y b b b ++ a 2 67 6 89 6 14 3 I a = (c) 312 I II << therefore rotation about the1-axis is unstable (see discussion Sec. 9.4)
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