Analytical Mech Homework Solutions 158

Analytical Mech Homework Solutions 158 - 2 2m 2 r 3 + Cr 2...

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2 32 20 2 rC r m −+ = DD A 2 2 22 r mr = D D A And with 2 sin mr φ α = ± A 1 2 2 1 sin mr  =   D D ± From Prob. 10.23, 2 3 cos mr mg mr =− A ±± For small oscillations about r , rr D ε = + D . r = 3 33 3 11 1 3 r r r   =+≈−     DD D D 2 3 3 1c mm mr r o s g A 43 3 cos mr mr g εα +=− AA 24 2 2 3s i n mr T ππ π ωφ == = D D ± A 1 3 10.25 () 2 2 1 xy m L mv qv A x y z q xA yA zA =+ + ++ + G G ± ± z x L mx qA x ± ± , x dA dL mx q dt x dt ± Using the hint, xxx dA A A A xyz dt x y z ∂∂∂ =++ ± x y x z A A LA qx y z x ∂∂ + ± y x z A AAA A A mx q x y z q x y z x yz + + ± ± y xx A A mx q y z z x x ∂   ± ± GG zy qy A z A  × × ± ± =∇ G G ( ) x qv A × G 20
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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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