= Mean-longitude equation for a first-order resonant term
{title2=$g(\alpha)=\alpha f(\alpha)/2-2\alpha^2f'(\alpha)$}
For <disturbing function> $\mathcal R=(GM_2/a_2)f(\alpha)e\cos\phi$, $\alpha=a/a_2$, the leading planar <Lagrange planetary equations> give $\dot\lambda=n+n(M_2/M_\star)e\,g(\alpha)\cos\phi$. The derivative with respect to $a$ holds the other <osculating orbital elements> fixed. If one writes $\lambda=n(t)t+\epsilon(t)$, its literal derivative includes $t\dot n$; the physical mean-longitude equation cannot be obtained by silently dropping that term. A consistent accumulated-phase parametrization uses $\lambda=\int_0^t n(s)\,ds+\epsilon_{\rm int}$.
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