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See, that's murky. For a properly defined Hamiltonian, you ought to have potential energy defined as independent of velocity, yet forklift theory allows 'lifting' (a Lie group acting a bit like a ladder operator) whilst moving and even accelerating[0] (left as an exercise to the reader). It's clearly an open system without total energy(t) constraint, though a more realistic model removes infinities by adding finite parameters, like LPG pressure or electric charge. [0] - EDIT/addendum: It has to be stated that an OSHA-compliant operator can only apply lift/lower operator while velocity is zero. Toy-model (think phi-4 field) is a lot more permissible.