On Nonlinear Dynamics of the Pendulum with Periodically Varying Length

Details On Nonlinear Dynamics of the Pendulum with Periodically Varying Length On Nonlinear Dynamics of the Pendulum with Periodically Varying Length

2009-10-20

arxiv.org/abs/0910.3802v2

Physics

Mathematical Physics

8 pages, 8 figures

Scientific paper

Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to periodic law is studied. This is the pendulum with periodically varying length which is also treated as a simple model of child's swing. Asymptotic expressions for boundaries of instability domains near resonance frequencies are derived. Domains for oscillation, rotation, and oscillation-rotation motions in parameter space are found analytically and compared with numerical study. Two types of transitions to chaos of the pendulum depending on problem parameters are investigated numerically.

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