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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
