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Dead object gravity

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I'm trying to get the basics of a gravity engine introduced in my game and I'm stuck with the first object I intended to tackle: a tree. I'd like to specify the objects the tree is made up from (root, branches, leaves) and let the physics engine derive how the branches should be hanging. Fromthat, I'd make a simplified model with less nodes etc. to make it bearable to render. I'm a bit confused how most physics engines work (newton, bullet) and how to integrate them - in specific, how to set up a joint that allows movement in any direction and that applies inverse force to keep the joint essentially enforced. Any ideas for any given physics engine? Is this something very unusual to want? Am I just using the wrong keywords?

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