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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