Find the normal modes of oscillation for small-amplitude motions of a double pendulum (a lower mass (m)

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Find the normal modes of oscillation for small-amplitude motions of a double pendulum (a lower mass \(m\) hanging from an upper mass \(M\) ) where the pendulum lengths are equal. Find the normal mode frequencies and the amplitude ratios of \(M\) and \(m\) in each case. Let the generalized coordinates be \(\theta_{1}\), the angle of the upper mass relative to the vertical, and \(\theta_{2}\), the angle of the lower mass relative to the vertical.

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Modern Classical Mechanics

ISBN: 9781108834971

1st Edition

Authors: T. M. Helliwell, V. V. Sahakian

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