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[Václav Šmilauer <eu@xxxxxxxx>]

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