This is basically rigid body dynamics. I am sure there are many libraries that can handle this. For example, this might help: https://github.com/projectchrono/chrono
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My first thought would be algodoo (formerly phun) via wine if you want an intuitive graphically driven 2d physics simulator/sandbox
I don't know about installed software, but Open Constructor is a recreation of the Soda Constructor, which is what that animation makes me think of: https://peterfidelman.github.io/constructor/
And here's another SodaPlay inspired tool as well: https://panoramx.ift.uni.wroc.pl/~maq/constructor/
Hope it helps!
Seems like a good fit for processing maybe?
Man, it's been years since I looked at Processing. I forgot it exists. This could be a good option.
Wouldn't you be able to do this in blender?
Yes, but I don't think it really works well with multiple constraints like that.
You could probably do keyframe animation on geometry, but I think bones only do trees.
No idea. I've been meaning to try blender again at some point anyway. I'll have to look into it.
Would second Blender. Plus if you're planning on maybe 3D printing a model with certain gyroscopic properties it's easy to export the model from there 😉
Check out modelica open source physical modeling language and the rigid body model library https://openmodelica.org/
I'm sure that you could use MetaPost to procedurally generate a frame, then merge them into an animation.
A newer, similar language is Asymptote, and it looks like it has animation support.