= Asymmetric resonant-argument libration
Libration about a resonant phase distinct from the symmetric values zero and $\pi$. For example, in a negative-Kepler-curvature reduction with disturbing potential $R=A\cos\phi+B\cos2\phi$, $A>0$, $B>A/4$, stationary points obey $\sin\phi(A+4B\cos\phi)=0$. At $\pi$, $R''=A-4B<0$, so it is unstable, whereas at $\cos\phi=-A/(4B)$ one has $R''=4B-A^2/(4B)>0$, giving two stable asymmetric centres. Actual branch thresholds depend on the resonance coefficients and evolving <orbital elements>.
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