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# 208 a total time of 0478 and a nal value of 535 rad

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Unformatted text preview: q1 changes stop the process print value of r print value of i*e (final time) print value of q This program yields a ﬁnal r value of about 0.208, a total time of 0.478, and a ﬁnal θ value of 5.35 rad ≈ 306◦ . Concerning the general dependence of these three quantities on m, M , g , and r0 (the initial r value), dimensional analysis says that The velocity is y = a2 (2t − T ), so the action is ˙ T L = = 12 2 a2 4t − 4T t + T 2 − ga2 t2 − T t 2 0 1234 1 1 m a2 T − 2 + 1 − ga2 T 3 − 2 3 3 2 mT 3 2 (a2 + ga2 ). 6 m dt 71 = 6.28. Three falling sticks Let θ1 (t), θ2 (t), and θ3 (t) be deﬁned as in Fig. 17. As noted in the solution to Problem 6.2, it is advantageous to use the function of a2 gives a2 = −g/ and Taking the derivative to minimize this small-angle approximations ﬁrst, 2. then take derivatives to ﬁnd the speeds. This strategy shows that all of the masses 6.32. Always a minimumhorizontally. Using sin θ ≈ θ, we have initially move essentially (308) m θ3 Let y0 (t) be the function ≈ −rθyields the stationary value of the action. (We know θ2 m that ˙ x1 =⇒ x1 ≈ −rθ1 , 1 that y (t) = −gt2 /2 + a1 t...
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