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[Fu zuoguang <question245062@xxxxxxxxxxxxxxxxxxxxx>]

Question #245062 on Yade changed:
https://answers.launchpad.net/yade/+question/245062

    Status: Answered => Open

Fu zuoguang is still having a problem:
Dear Bruno Chareyre and Jan Stránský:

      I am sorry for the lost details in my last description of my
question, which can be defined as 'the relative motion of two rigid
spheres at a contact point' .

      Fig 1 : http://imageshack.com/a/img20/111/oh517.jpg

      As shown in Fig 1, with the purpose of defining the motion paths
of the two rigid spheres, two types of motion frames should be employed
to work together. One is global frame, of course, Cartesian coordinates
in 3D space, and the other is here called the 'reference frame', which
is composed of the original point (contact point) and the tangent plane
of the two contact bodies.

      So, the motion of one sphere caused by its resultant velocity
(linear velocity and angular velocity) can be divided into two parts:
its relative motion in reference frame and reference frame motion in
global space. The entire task I should do for getting the correct
tangential displacement of the two bodies is just to calculate its first
part caused by relative motion and then the second part determined by
reference frame motion.

      In the initial state, the known variables of the two spheres are
shown in Table 1 (all the variables are just defined in global space):

      Table 1 : http://imageshack.com/a/img809/8876/h9lo.jpg

      With the support of 'Yade document' and luding[2008], the
calculation processes are all in Fig 2.

      Fig 2 : http://imageshack.com/a/img541/7540/8qsj.jpg

      There is nothing different between what I just described above and
that just in luding[2008]. But my troubles are surely in the second step
work, to calculate the reference frame motion and then the tangential
displacement caused by it. Following my own conception above, it can be
calculated as Fig 3.

       Fig 3 : http://imageshack.com/a/img18/8033/hiso.jpg

       My troubles are that
       (1). Are there something wrong in my comprehension from equations (1) to (10) ?
       (2). Is the formula (10) equal to the formula (11)? If yes, how to build the equality relationship between the two, in other word, how to obtain the formula (11) from the known formula (10)? If no, please tell me the reasons.

       Seek your help!

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