result; see Eq. (3.45) of [@bd]).

From the result (\[seventeen\]) above, we can easily derive the following explicitly DSX-like expression for the total linear momentum of the $N$-body system: $$\begin{aligned}
 p_i(t) &=& \sum_A\biggl\{ M^A v_A^i\left[1+{1 \over c^2}\left(
  {1 \over 2}v_A^2+G_A^{\prime\prime} \right)\right] + {1 \over c^2}
  a_A^j
  s_A^{ij} - {3 \over c^2} {d \over dt} \left(a_A^j m_A^{ij}\right)
  \nonumber \\
 & &  - {1 \over c^2} z_A^i \sum_l {1 \over l!}
  \left[l M_L^{A (1)} G_L^{A\prime}+\left(l+1\right)M_L^A G_L^{A (1)
  \prime}\right]
  - {1 \over c^2} \left(v_A^i z_A^j - \delta_{ij}
  {\bf v}_A.{\bf z}_A\right) R^j_{A a} \sum_l {1 \over l!} M_L^A
  G_{aL}^{A\prime}  \nonumber \\
 & &  - {1 \over c^2} \left(z_A^i z_A^j - {1 \over 2}
  \delta_{ij} z_A^2 \right) R^j_{A a} \sum_l {1 \over l!} {d \over
  dT_A} \left(M_L^A G_{aL}^{A\prime}\right)
 - {2 \over c^2} z_A^j R^i_{A [a} R^j_{A b]}
  \sum_l {1 \over l!} {d \over dT_A} \left(M_{aL}^A G_{bL}^{A\prime}
  \right) \biggr\} \nonumber \\
 & & + \sum_A \biggl\{ {d \over dT_A} \left(m^i_A\right)\left(1+{2
  \over c^2} G_A^{\prime\prime} \right) + {1 \over c^2} v_A^j {d
  \over dt}
  \left(m^j_A v_A^i\right) + {1 \over c^2} m^i_A {d \over dT_A}
  G_A^{\prime\prime} - {2 \over c^2} v_A^i m^j_A a_A^j\biggr\}
 \nonumber \\
 & &  + {\cal O}(4) \;. \label{twentyone}\end{aligned}$$ Again, the last sum of terms in 