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I dw'/dt + w' cross Iw' = T'
when (.)' is value (.) in local r.f. This equation don't integrated by
simple leap-frog, because we will have w' on right.
So, problem is not only in a rotation of vectors. We need also other
integration algorithm for clumps.
Is this correct?
Yes, I think this is correct. And this non linear equation cannot be
It needs an iterative procedure for each clump at each time-step (1),
and of course a matrix representation of I.
For low-spin rotations however, one can neglect the term in w'^2. If
aditionally, you neglect out-of-diagonal terms in I (or if I is given in
principal axis), then you can use a simpler algorithm and leap-frog
still applies (2) (and you use a vector representation of I).
This approximation is proposed as an option for clumps in PFC3D.
We could perhaps make sure that situation (2) is handled correctly first
(with current definition of inertia*, it doesn't need big changes, if
any), before going to situation (1). Is somebody planning to simulate
high-spin clumps by the way?
(*) Sorry Vaclav, I should have check the definition of inertia before
claiming it was that of a sphere. You develop too fast for me! ;)
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