What is it about?
The solution of the standard integral for the period is given as a power series. This is compared with the expansion of the standard "small amplitude" result and six other expressions of increasing complexity but also greater accuracy, confirmed by numerical integration.
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Why is it important?
The simple inclusion of a cos term to the standard result produces an accuracy of better than 1% for acute angle swings. The approach used might be applicable to other "standard" results.
Perspectives
This is about an integral whose integrand has zero change in its odd derivatives over the range of integration. Estimating the errors in their numerical integration is fascinating.
Robin Murphy
Read the Original
This page is a summary of: 101.46 Improved simple pendulum results, The Mathematical Gazette, October 2017, Cambridge University Press,
DOI: 10.1017/mag.2017.148.
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