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Suggestions needed for gravity and physics applied to hair system

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Hi guys, I have developed an application that allows to style hair on a human 3D model.
At this point I'd like to add some simple physics and gravity so that when the model is posed, hair react accordingly.
I'm already capable of testing hair collision with the underlying 3D model, so that the hair do not get sunk into the mesh; also, I'm not interested in performing gravity and physics in real time (the user will have to click a button to start the calculations).

So, how'd approach this matter (which I believe is quite complex)?
Given that I have a hair system where each hair has a set of properties (vertices, elasticity etc.), I assume that I need to run a time-based routine that at each step calculates the new hair vertices affected by gravity, friction etc. But what math shall be used in that regard?

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