Dynamics of the pendulum with periodically varying length

Anton O. Belyakov (1) , Alexander P. Seyranian (1) , Angelo Luongo (2)

1 Institute of Mechanics
2 DICEAA - Dipartimento di Ingegneria Civile, Edile-Architettura, Ambientale

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 a 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 a numerical study. Chaotic motions of the pendulum depending on problem parameters are investigated numerically.

Domaines: Mécanique [physics.med-ph]

Anton O. Belyakov, Alexander P. Seyranian, Angelo Luongo. Dynamics of the pendulum with periodically varying length. Physica D: Nonlinear Phenomena, 2009, 238 (16), pp.1589-1597. ⟨hal-00788480⟩