Analytical Mech Homework Solutions 133

Analytical Mech Homework Solutions 133 - (I I ) (I I ) 2 2...

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() ( ) 12 31 22 11 3 2 13 32 0 II I ωωω −−  +− + =   ±± ω 1 0 K += , ( )( ) ( )( ) 3221 3231 3 I III IIII K ωω  =− +   (a) For 3 large and 2 0 = , so 1 0 K > 1 0 K + = is the harmonic oscillator equation. 1 oscillates, 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 3 0 = and 2 large, 1 0 K < so 1 0 K + = is the differential equation for exponential growth of 1 with time: 1 1 kt Ae Be =+ 1 = . Motion is unstable for the initial rotation mostly about the principal axis having the median moment of inertia. 9.20 0 since either xy i i i i Im x y = i x or is zero for all six particles. Similarly, all the other products of inertia are zero. Therefore the coordinate axes are principle axes. i y ( 0,0,c
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.

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