()()()12312211321213320IIIIIIIIIωω ω−−+−+=±±ω ω1110Kωω+=±±, ()()()()32213231221231312IIIIIIIIKI II Iωω−−−−= −+(a) For 3ωlarge and 20ω=, so 10K>1110Kωω+=±±is the harmonic oscillator equation. 1ωoscillates, but remains small. Motion is stable for initial rotation about the 3 axis if the 3 axis is the principal axis having the largest or smallest moment of inertia. (b) For 30ω=and 2ωlarge, 10K<so 1110Kωω+=±±is the differential equation for exponential growth of 1ωwith time: 11k tk tAeBeω−=+1=. Motion is unstable for the initial rotation mostly about the principal axis having the median moment of inertia. 9.200 since either xyiiiiIm x y=∑ixor is zero for all six particles. Similarly, all the other products of inertia are zero. Therefore the coordinate axes are principle axes.
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