s1110b - ADVANCED DYNAMICS — PHY 4241/5227 HOME AND CLASS...

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Unformatted text preview: ADVANCED DYNAMICS — PHY 4241/5227 HOME AND CLASS WORK – SET 7 Solution for assignment 10b: Double Pendulum (continuation of 10). For small oscillation we have derived the Euler-Lagrange equations, which read in matrix notation ¨ 21 φ 2g/l 0 φ = 0. ¨+ 11 ψ 0 g/l ψ This is solved by the exponential ansatz (physical is the real part of the solution): Φ(t) = φ ψ = ei ω t φ0 ψ0 −2ω 2 + 2g/l −ω 2 2 −ω −ω 2 + g/l 0 = det with eigenmodes ¨ φ ¨ ψ ⇒ φ ψ −2ω 2 + 2g/l −ω 2 −ω 2 −ω 2 + g/l ω± = g l 2± = −ω 2 ei ω t = 0. = ω4 − √ 2. φ0 ψ0 4g 2 2g 2 ω+ 2 l l ...
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This note was uploaded on 11/10/2011 for the course PHY 4241 taught by Professor Berg during the Spring '11 term at University of Florida.

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