技術者教育のための工学数理の力学教材の改定(32):アルキメデスの楕円コンパスによる振子の自由振動

概要

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A pair of trammels, called trammel of Archimedes, work as a pendulum under the action of gravity. Theiroscillation mechanism is revealed mechanically based upon the equation of motion. Numerical analysis is also used toshow their typical features. When it draws a circle, the period increases from 2π, as initial angle becomes large. This isjust the case of simple pendulum. When it draws a long ellipse, the period decreases from 2π, reaches a minimum andthen increases, as initial angle becomes large. This may be one of typical features. Nonlinear oscillation is analyzed by themethod of harmonic balance and the method of multiple scales.
2013-01-31