Hi Jason
The issue here is that the hydrodynamic forces (not just moments)
have a contribution from the rotational
accelerations (and not just the translational accelerations) at
the outset
(and
vice-versa) , so the inertia matrix
(after moving this acceleration-dependent "mass matrix" to the
LHS) is never just a 3x3.
A similar "6x6" inertia matrix crops up in pydy already when the
barycentre isn't used for the origin -
but then I think it comes out of ref frame transformations where
the cg is offset in a subsequent frame
from the usual original barycentric ref frame origin so is not set
up as such at the outset of the analysis
- but I'd need to let the system know about rotation/translation
"coupling" at the outset if the added mass
is to be used.
The mass matrix generated in KanesMethod and LagrangesMethod is in
terms of the generalised coordinates
while the added mass matrix I wish to use at the outset is defined
in body axes like the present (conventional)
inertia Ixx, etc terms. I wish to use KanesMethod to incorporate
the added mass terms in the final equation set
for the EOM in terms of the generalised coordinates.
Hope this is a bit clearer - if not let me know.
I've tried to find a paper via Google where someone has tried this
for Kane's method. The only one I've found
https://books.google.com/books?id=YwfaBwAAQBAJ&pg=PA207&lpg=PA207&dq=kane+added+mass&source=bl&ots=Me9oZsfh9l&sig=mxKziYRQEEW-gk3a9MiPEIc6eDY&hl=en&sa=X&ved=0CD4Q6AEwBWoVChMIhLOx3ZizxwIVCWvbCh13cQCu
is where the authors make the assumption that the off-diagonal
terms in the added mass matrix are negligible,
so the extra terms are easily incorporated in the present
framework, although the earlier analysis (eqn 18) seems
more general. I'm looking for an implementation of this more
general approach for pydy.
Kind regards
Steve