Growth rate of a pendulum with a time-varying length

Zhifei Zhang

doi:10.1117/12.2679216

14 June 2023 Growth rate of a pendulum with a time-varying length

Zhifei Zhang

Proceedings Volume 12725, International Conference on Pure, Applied, and Computational Mathematics (PACM 2023); 127250M (2023) https://doi.org/10.1117/12.2679216
Event: International Conference on Pure, Applied, and Computational Mathematics (PACM 2023), 2023, Suzhou, China

Abstract

Stability of non-autonomous system is in general difficult to analyze and the frozen in time assumption is known to break down in high dimensional system. This work proposes another criterion to analyze the stability of non-autonomous system by obtaining its upper bound on the energy growth. The computation of upper bound is then formulated as a convex optimization problem based on linear matrix inequality. We also perform pendulum experiments with a linear varying or oscillating length to analyze its stability. The experimental results demonstrate that the time-varying length of pendulum will lead to a growing oscillation amplitude of pendulum and the associated growth rate also agree well with the upper bound prediction based on the linear matrix inequality. This work provides a new analysis framework to analyze stability of non-autonomous system.

Citation Download Citation

Zhifei Zhang "Growth rate of a pendulum with a time-varying length", Proc. SPIE 12725, International Conference on Pure, Applied, and Computational Mathematics (PACM 2023), 127250M (14 June 2023); https://doi.org/10.1117/12.2679216

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