2007/07/06 by I. R. Gatland, Ian R. Gatland, Gatland, Ian R.
Engineering · Physics and Astronomy · #Classical Physics (physics.class-ph) #Control and Dynamics of Mobile Robots #Experimental and Theoretical Physics Studies #FOS: Physical sciences #physics.class-ph
paper · pdf · doi:10.48550/arxiv.0707.1029
9 pages (including references and a table)
arxiv created 2007/07/06 · openalex publication_date 2007/07/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The standard series expansion for the period of a finite amplitude pendulum as a function of energy (and hence amplitude) provides a lower limit on the period when the series is truncated. An adjustment to the last term in the truncated series to take account of the dropped terms improves the accuracy of the approximation and provides an upper limit on the period. More accurate approximations can then be obtained using intermediate expressions.