s11f1025

s11f1025 - ADVANCED DYNAMICS — PHY 4936 HOME AND CLASS...

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Unformatted text preview: ADVANCED DYNAMICS — PHY 4936 HOME AND CLASS WORK – SET 5 Solution for assignment 25: Normal Modes of Double Pendulum (continuation of 8). 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 0 = det −2ω 2 + 2g/l −ω 2 −ω 2 −ω 2 + g/l g l 2± = −ω 2 ei ω t φ ψ −ω 2 −ω 2 + g/l with eigenmodes ω± = ¨ φ ¨ ψ ⇒ √ = 0. = ω4 − 2. φ0 ψ0 4g 2 2g 2 ω+ 2 l l ...
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This note was uploaded on 12/11/2011 for the course PHY 4936 taught by Professor Berg during the Fall '11 term at FSU.

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