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twist/bend increment computation

 

Hi there,

please someone with more spatial intelligence than me could explain how to compute twist and bending (i.e. relative rotation) increment between two spheres? Both of the spheres can be moving at the same time (that also moves the contact line), they can have different radius. I know their velocities, angular velocities, how the contact normal changes... At the same time, I need that it is orthogonal to shear, i.e. when points on the sphere surfaces stay in the same relative position, there will be no shear.

I thought that it could be computed from the symmetric/antisymmetric split of relative displacement at contact point, along the lines

u₁=v₁+ω₁×(c-x₁), u₂=v₂+ω₂×(c-x₂).

Then shear displacement would be 2× the antisymmetric part (that is the current formulation in ScGeom for instance), and bending would be 2× the symmetric part (removing rigid interaction rotation, which is the ugly term at the end), i.e.

us=2⋅(u₁-u₂)/2, φ=|x₂-x₁|⋅2⋅[(u₁+u₂)/2-((x₂-x₁)/|x₂-x₁|)×(v₂-v₁)]

Does that make sense? Or is there a better way?

Thanks a lot.

v




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