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Analytical Mech Homework Solutions 140

Analytical Mech Homework Solutions 140 - L = mg z L L = = 0...

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0 L L x y = = , L mg z = − From equations 10.4.5 … 0 i i L d L q dt q = ± , 0 mx = ±± mx const = ± , 0 my = ±± my const = ± mz mg = − ±± 10.3 Choosing generalized coordinate x as linear displacement down the inclined plane (See Figure 8.6.1), for rolling without slipping … x a ω = ± 2 2 2 2 2 1 1 1 1 2 7 2 2 2 2 5 10 x T mx I mx ma mx a ω  = + = + =   ± ± ± 2 ± For V at the initial position of the sphere, 0 = V m sin gx θ = − 2 7 sin 10 L T V mx mgx θ = = + ± 7 5 L mx x = ± ± , 7 5 d L mx dt x = ±± ± sin L mg x θ = 7 sin 5 mx mg θ = ±±
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