Analytical Mech Homework Solutions 186

Analytical Mech Homework Solutions 186 - 23 K (1 + 2 m M )...

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23 () 2 2 3 12 mM KK mm M m ω + == + + 11.24 y 2 a a α α M x 2 m y 1 x 1 y 3 x 3 m Select coordinates ( x i , y i ) as shown, then … 2222 2 2 1133 11 22 Tm xyxy M xy =+ + + + + ±±±± ±± The potential energy depends only on the compression (or stretching) of the two springs connecting each m to M (hydrogen to sulfur). Let 1 a δ and 2 a be incremental changes in the distances a or and or . We have … 1 (1 2) HS 2 a (3 HS 2) () () 2 2 1 1 2 2 1 sin cos 2 ax x yy x xyy δα α =− +− = −+− 1 3 2 3 2 3 2 1 sin cos 2 x y y x x y y = 3 ()() 1 2 Vka a δδ   We can reduce the degrees of freedom from 6 to 3 by ignoring the two translational modes and the rotational mode.
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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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