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M2M translation formula

The multipole moment centred O' is given by (See (3.53) and (3.54))
  
M1j,n,m(O') = $\displaystyle \int_{S_y} C_{cdjl} \frac{\partial}{\partial y_l}
R_{n,m}(\overri...
...th$ y $ }}) \phi_d(\mbox{\boldmath$ y $ }) n_c(\mbox{\boldmath$ y $ }) dS_{y} ,$ (H.1)
M2n,m(O') = $\displaystyle \int_{S_y} C_{cdjl} \frac{\partial}{\partial y_l}
((\overrightarr...
...dmath$ y $ }}))\phi_d(\mbox{\boldmath$ y $ }) n_c(\mbox{\boldmath$ y $ }) dS_y.$ (H.2)

Substituting (E.2) into (H.1) we obtain

\begin{eqnarray*}M^1_{j,n,m}(O')&=&\sum_{n'=0}^{n}\sum_{m'=-n'}^{n'}R_{n',m'}(\o...
...-m'}(O)- (\overrightarrow{OO'})_j M^1_{j,n-n',m-m'}(O)\right).
\end{eqnarray*}




Ken-ichi Yoshida
2001-07-28