I encountered a necessary optimality conidtion involving growth rate of Lagrange multiplier in this note on Ramsey model
$$\frac{\dot \lambda}{\lambda} = \mathcal {v} - (f^\prime(k)-\delta-\xi)$$
in which $\mathcal {v}$ is the time preference rate, $\xi$ is the population growth rate, and $\delta$ is the depreciation rate.
Is there some way to make sense of it in a similar fashion as Euler equation?