= Angular momentum deficit
{title2=$\mathrm{AMD}=\sum_j L_j(1-\sqrt{1-e_j^2}\cos I_j)$}
= AMD
{c}
{synonym}
The difference between the <angular momentum> of circular coplanar orbits at fixed <semi-major axes> and the system's actual angular momentum along the reference normal. With circular momenta $L_j=m_j\sqrt{GM_\star a_j}$ it is $\sum_jL_j(1-\sqrt{1-e_j^2}\cos I_j)$. For small planar <orbital eccentricities> its quadratic part is $\frac12\sum_jL_j|z_j|^2$. Its conservation in $\dot z=iAz$ requires $L_jA_{jk}=L_kA_{kj}$.
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