yade-dev team mailing list archive

[Janek Kozicki <janek_listy@xxxxx>]

Václav Šmilauer said:     (by the date of Wed, 01 Dec 2010 15:27:03 +0100)

> 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?

sorry to be boring, but why not use quaternions for twist/bending,
what's wrong with it?

IMO shearing is a separate issue and there is no point in calculating
shear as being antisymmetric to bending. That might be the case in
2D, but in 3D+twisting when contact point could revolve around some
axis? I'm not so sure.

also, I don't know what is the meaning of symbols that you used in
formulas above: v₁,ω₁,x₁, etc...

-- 
Janek Kozicki                               http://janek.kozicki.pl/  |