due to the unavoidable intervention of nonlinear, interbody gravitational effects. Mathematically, this complication manifests itself through the occurrence of “bad” DSX moments $(N_L,P_L)$. It has been, however, possible to reach a successful formulation of the individual rotational laws of motion through a carefully adjusted definition of the individual spin of each body [@dam3]. In the following, we briefly address the problem of breaking up the total angular momentum into a sum of contributions which make sense within the DSX framework.

The global angular momentum of the system reads ([@fo], [@di1], [@dam3]) $$\begin{aligned}
 s_i(t) &=& \epsilon_{ijk} \int d^3x\, x^j \biggl\{ \sigma^k \left[1+
  {4 \over c^2} w\right] \nonumber \\
 & & \qquad\;  - {\sigma \over c^2} \left[4 w^k + {1 \over 2}
  \partial_k \partial_t z(x,t)\right]\biggr\} + {\cal O}(4) \; ,
 \label{twentyfour}\end{aligned}$$ where $z(x,t) = G \int d^3x^\prime \,\sigma(x^\prime,t) |{\bf x} -
{\bf x}^\prime |$. For an isolated system of arbitrary bodies it has been previously shown that $s_i(t)$ is conserved at the post-Newtonian level.

In order to preserve the post-Newtonian accuracy \[i.e. modulo ${\cal O}(4)$\] of the result, one needs the transformation law of the global mass current $\sigma^k(x)$ to local coordinate quantities with corresponding precision. After some algebra one arrives at 