i.e. the value of L may be considered as a square of Euclidian distance between a current state of the system and its equilibrium. If this distance decreases with time (i.e. the derivative dL/dt < 0 along any system's trajectory), then in accordance with the Lyapunov stability theorem we have hoped that the system goes to the stable equilibrium. Note that I speak of "hope", since we have to test all the trajectories (or a statistically "sufficient" large number of them) in order to be able to speak correctly about stability
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