Study on the variable length simple pendulum oscillation based on the relative mode transfer method

Abstract

In this study, we employed the principle of Relative Mode Transfer Method (RMTM) to establish a model for a single pendulum subjected to sudden changes in its length. An experimental platform for image processing was constructed to accurately track the position of a moving ball, enabling experimental verification of the pendulum’s motion under specific operating conditions. The experimental data demonstrated excellent agreement with simulated numerical results, validating the effectiveness of the proposed methodology. Furthermore, we performed simulations of a double obstacle pendulum system, investigating the effects of different parameters, including obstacle pin positions, quantities, and initial release angles, on the pendulum’s motion through numerical simulations. This research provides novel insights into addressing the challenges associated with abrupt and continuous changes in pendulum length.

Time-Optimal Motions of a Mechanical System with Viscous Friction

“…In case (1), a constant control equal to 1 is maintained throughout the entire time interval. Case (2) is not possible, as ψ 2 (T) < 0 and does not satisfy condition (16).…”

“…The pendulum with periodically varying length which is also treated as a simple model of a child's swing is investigated in [15]. Simulations were performed in [16] on a double obstacle pendulum system to investigate the effects of various parameters, including the positions and quantities of obstacle pins, and the initial release angles, on the pendulum's motion through numerical simulations. The pendulum with vertically oscillating support and the pendulum with periodically varying length were considered as two forced dissipative pendulum systems, with a view to draw comparisons between their behavior [17].…”