Littlewood, J.E. (1964) Adiabatic Invariance IV: Note on a New Method for Lorentz’s Pendulum Problem. Annals of Physics, 29, 13-18. http://dx.doi.org/10.1016/0003-4916(64)90189-7

has been cited by the following article:

• TITLE: Bessel Function and Damped Simple Harmonic Motion

  AUTHORS: Masoud Asadi-Zeydabadi

  KEYWORDS: Bessel Function; Simple Harmonic Motion; Damped Sinusoidal Function; Lengthening Pendulum; Spring-Mass System; Lagrange Polynomial

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.2 No.4, March 13, 2014

  ABSTRACT: A glance at Bessel functions shows they behave similar to the damped sinusoidal function. In this paper two physical examples (pendulum and spring-mass system with linearly increasing length and mass respectively) have been used as evidence for this observation. It is shown in this paper how Bessel functions can be approximated by the damped sinusoidal function. The numerical method that is introduced works very well in adiabatic condition (slow change) or in small time (independent variable) intervals. The results are also compared with the Lagrange polynomial.