The lengthening pendulum: Adiabatic invariance and bursting solutions

Sahu, Subhayan and Pai, Shriya and Manjunath, Naren and Balakrishnan, Janaki (2021) The lengthening pendulum: Adiabatic invariance and bursting solutions. Physics Open, 7 (100067). pp. 1-7.

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Abstract: The adiabatic invariance of the action variable of a length varying pendulum is investigated in terms of the two different time scales that are associated with the problem. A length having a general polynomial variation in time is studied; an analytical solution for a pendulum with length which varies quadratically in time is obtained in the small angle approximation. We find that for length with quadratic time variation, the action neither converges (as it does for linear time variation), nor diverges (as it does for exponential time variation), but rather shows oscillatory behaviour with constant amplitude. It is then shown that for a pendulum length which has a combination of periodic and linear time variations, the action is no longer an adiabatic invariant and shows jumps with time. In the case in which the length varies sinusoidally in time, we demonstrate that the full nonlinear system exhibits bursting oscillations.
Item Type: Journal Paper
Additional Information: Copyright belongs to the Publisher.
Keywords: Lengthening pendulumAdiabatic invarianceAction variableBursting oscillation
Subjects: School of Natural and Engineering Sciences > Complex Systems
Programmes > Complex Systems Programme
Date Deposited: 16 Apr 2021 11:11
Last Modified: 16 Apr 2021 11:18
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    Funders: JB-SERB, DST, GOI.SS, SP and NM were each supported by KVPY National Fellowships from the DST, GOI, at the Dept. of Physics, IISc., Bangalore, during an earlier stage of this work
    Projects: Project File No. MTR/2018/000797

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