Problem on the time evolution of the particle?

Dear all:
I am confused about the time evolution of the particle given in the reference: C. Aidun and J. Clausen, Lattice Boltzmann Method for Complex Flows. Annual Review of Fluid Mechanics, 2010. 42(1).

I . d(W)/dt + W x [I . W ] = T

I think that the angular momentum is I.W, so the equation should be d(I.W)/dt = I . d(W)/dt = T.
So I do not know the meaning of W x [I . W ]. I am very glad if anyone could you give an explanation. I need your kind help and thanks in advance.

Best Regards



it depends on the coordinate system you are talking about. The equation is different in the lab frame and in the co-rotating coordinate system.
You should have a look at a mechanics textbook where rotating bodies are covered.


Hello, dear Timm. Thanks a lot for your help.

Yes, as the angular momentum (I.W) is described in the rotating system, d(I.W) /dt is not equal I.dw/dt.