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[Alexander <question271301@xxxxxxxxxxxxxxxxxxxxx>]

New question #271301 on Yade:
https://answers.launchpad.net/yade/+question/271301

Hello everybody.

Can anyone help me to understand the computation of relative shear displacement u_s in the interaction of 2 spheres  via relative shear velocity u'_s as it's described in [Bourrier2013] (http://i11.pixs.ru/storage/1/6/6/picJPG_1860466_18763166.jpg):  

u'_s = O'_1 − O'_ 2 +(O_1 −C)xω_1 −(O_2 −C)xω_2, where O'_i - derivatives of spheres' center radius vector. ω_i and C - angular velocities and contact point  in the timestep t + d_t.

so as i understand the displacement  u_s computes incrementally using small time step d_t,  u_s = int_(0)^(d_t) u'_s  dt =
= (O_1 - O-_1)  − (O_ 2 - O-_2) + ((O_1 −C)xω_1 −(O_2 −C)xω_2) * d_t, where O_i - is the coordinates of centers in step t + d_t, and O-_i is the previous position of spheres centers.

the displacement u_s is a vector in the plane per-pendicular to the unit normal n of the interaction. 

So the vector ((O_1 −C)xω_1 −(O_2 −C)xω_2) * dt is per-pendicular to n because of (O_i −C)xω_i is a vector product and (O_i −C) is parallel to n.

the trouble is that the vector (O_1 - O-_1)  − (O_ 2 - O-_2) is not per-pendicular to normal n? So where i'm wrong in my consideration.

with regard, Alexander


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