  For isentropic fluids, dynamical evolution of a binary system conserves the
baryonic mass and circulation; therefore, sequences of constant rest mass and
constant circulation are of particular importance. In this work, we present the
extension of our Compact Object CALculator (\cocal{}) code to compute such
quasiequilibria and compare them with the well-known corotating and
irrotational sequences, the latter being the simplest, zero-circulation case.
The circulation as a measure of the spin for a neutron star in a binary system
has the advantage of being exactly calculable since it is a local quantity. To
assess the different measures of spin, such as the angular velocity of the
star, the quasilocal, dimensionless spin parameter $J/M^2$, or the circulation
$\mathcal{C}$, we first compute sequences of single, uniformly rotating stars
and describe how the different spin diagnostics are related to each other. The
connection to spinning binary systems is accomplished through the concept of
circulation and the use of the constant rotational velocity formulation.
Finally, we explore a modification of the latter formulation that naturally
leads to differentially rotating binary systems.
