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/ | _______________________________________________ Mailing list: https://launchpad.net/~yade-dev Post to : yade-dev@lists.launchpad.net Unsubscribe : https://launchpad.net/~yade-dev More help : https://help.launchpad.net/ListHelp