技術者教育のための工学数理の力学教材の改定(34):アルキメデスの楕円コンパスによる振子の外部励振

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. For tracing a circle, the period increases from 2π, as initial angle increases. This is just thecase of simple pendulum. For tracing a long ellipse, the period decreases from 2π, reaches a minimum and then increases,as initial angle increases. Nonlinear oscillation with softening/hardening due to the length ratio is analyzed for externalexcitation in horizontal and vertical directions by the method of harmonic balance and the method of multiple scales.
2013-01-31