  In the first half of this article, we survey the new quasi-local and total
angular momentum and center of mass defined in [9] and summarize the important
properties of these definitions. To compute these conserved quantities involves
solving a nonlinear PDE system (the optimal isometric embedding equation),
which is rather difficult in general. We found a large family of initial data
sets on which such a calculation can be carried out effectively. These are
initial data sets of harmonic asymptotics, first proposed by Corvino and Schoen
to solve the full vacuum constraint equation. In the second half of this
article, the new total angular momentum and center of mass for these initial
data sets are computed explicitly.
