技術者教育のための工学数理の力学教材の改定(22):バネ振子の非線形振動の数値解析

概要

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A spring-pendulum has two oscillation modes to arise independently near its static equilibrium state, whichare not coupled even in their nonlinear stage. When it starts from initial values away from the equilibrium, the pendulummakes nonlinear coupling oscillations and leads to very complicated motions in swinging and rotation and then to chaos.By examining the work by W. K Lee & H. D. Park ("Second-order approximation for chaotic responses of a harmonicallyexcited spring-pendulum system" International Journal of Non-Linear Mechanics, 34 (1999), pp.749-757), which we callCase (i), the method of multiple scales is applied to seek other model equations for Cases (ii), (iii) and (iv), where thedetuning parameter is different from the one that Lee & Park used. The results for Cases (i)-(iv) are compared with thatobtained from the original equations of motion and Case (iv) is found to give the best results.
2011-01-31