技術者教育のための工学数理の力学教材の改定(30): 変形Atwood 機械の運動の特異摂動法による解析

概要

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Atwood's machine is a representative device in mechanics, which George Atwood invented in 1784 as a laboratoryexperiment to verify the mechanical laws of uniformly accelerated motion. We revisited this mechanical deviceto make PBL (Problem Based Learning) resources and practice problems for computational dynamics in the advancedengineering course. In the book by Nayfeh & Mook (1995), introduced is Atwood's machine in which a body of massm1 is linked to two bodies of mass m2 with ropes through two pulleys. If m2/m1 < 1/2, it works as usual Atwood'smachine. If m2/m1 > 1/2, it works, however, as an oscillation machine around its equilibrium state. We call this "ModifiedAtwood's Machine" and make analysis for weakly nonlinear oscillation using the method of multiple scales and He'smodified Lindstedt-Poincar´e method. The angular frequency obtained by two terms expansion shows nice agreement.
2012-01-31