  The least action principle occupies a central part in contemporary physics.
Yet, as far as classical field theory is concerned, it may not be as essential
as generally thought. We show with three detailed examples of classical
interacting field theories that it is possible, in cases of physical interest,
to derive the correct field equations for all fields from the action (which we
regard as defining the theory), some of its symmetries, and the conservation
law of energy-momentum (this last regarded as ultimately coming from
experiment)
