Dev tools · September 18, 2016
Simple pendulum simulation with rational trigonometry
Context: I'm looking at Norman Wildberger's rational trigonometry[1], and here I was wondering how useful it is in physics. So I thought about testing it with the famous simple pendulum exercise. It's not obvious we get any FPS gain, but still I find it cool to even be able to get the same result differently. 1. https://en.wikipedia.org/wiki/Rational_trigonometry
Simple pendulum simulation with rational trigonometry launched on September 18, 2016 with 52 votes, #1,540 of 3,744 launches that month and more than 90% of that year's launches. The site was still online in September 2026, 10 years on.
In plain words
This project demonstrates a simple pendulum simulation solved using rational trigonometry, an alternative mathematical approach that avoids traditional trigonometric functions. It compares conventional methods with rational trigonometry to explore whether the alternative approach offers practical benefits like performance improvements. The simulation explores progressively complex pendulum problems, from simple to double and arbitrary configurations. Created for developers and physics enthusiasts interested in experimental mathematical methods, it's designed to test whether rational trigonometry provides useful advantages in physics calculations, even if performance gains aren't guaranteed.
written from the facts on this page · September 2026
From the sources
On this page I'll try to solve the two-dimensional pendulum problem in various ways, including using rational trigonometry . I'll start with the simple pendulum, and then maybe the double one and arbitrary long ones. With trigonometric functions, the speed \(v\) and elevation \(h\) become respectively \(\dot\theta\) and \(1 - \cos(\theta)\). which we can turn into a first order derivative by considering \(\dot{\theta}\) as an additional variable. The naive approach described above has a major issue : it can not deal with full swings. Indeed the point $$\lim_{\mu\to\infty}\mathrm{M}(\mu) = (-1, 0)$$ can never be reached with that parametrization. A simple solution is to switch to a different…from grondilu.github.io
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