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Hah, I did something similar over at https://ari.blumenthal.dev/!/-2/-1/three-body after reading the book last year.
Source over at https://github.com/zkhr/blog/blob/main/static/js/three.js
This is the source code for the popular ThreeBodyBot [0]
It contains a numerics tutorial [1] that au found very useful for my use case.
[0] https://github.com/kirklong/ThreeBodyBot
[1] https://github.com/kirklong/ThreeBodyBot/blob/master/Numeric... (ipynb)
Principia is extremely impressive, they document all their math here: https://github.com/mockingbirdnest/Principia/tree/master/doc...
One interesting detail is that the source code makes extensive use of non-ASCII identifiers, for mathematical symbols and for the names of mathematicians. One of the two primary contributors is also an active contributor to Unicode
A few years ago a friend and I made something similar to universe sandbox, though only with the gravitational simulation part: https://github.com/fayalalebrun/Astraria
Surprisingly enough the jar still runs without issue. Something which probably would not be the case for linux binaries, but maybe for windows.