I've been reading Landau and Lifgarbagez's Mechanics and have some issues I need clearing up, so I hope folk here can help :) It is stated that the Principle of Least Action is not always valid for the entire path of a system, but only for a sufficiently small segment...what does this mean? I interpret this as saying: "the action will not always be minimized (altho it usually is in most cases), but it may take on a maximum value. What is important is that it is an extremum. However, if we look at a sufficiently small part of ANY path, it will always be a minimum, but the entire path may not be" ....is this correct???