We show the equivalence of five different conditions on a classical field \(\psi \) with values in a restricted multicotangent bundle to be a solution of the field equations, notably in terms of the Hamilton-Volterra equations, the principle of least action, and several conditions based on the contraction of the multi-vector tangent to \(\psi \) with canonical differential forms. Most prominently, we have equivalence to the “dynamical Hamilton-de Donder-Weyl equation” that can be vastly generalized to define Hamiltonian dynamics on multisymplectic manifolds, defined for sources of different dimensions.