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

On Nonlinear Dynamics of the Pendulum with Periodically Varying Length