Newton's second law in field theory

In this article we present a natural generalization of Newton's Second Law valid in field theory, i.e., when the parameterized curves are replaced by submanifolds higher dimension. For it introduce what have called geodesic k-vector field, analogous to ordinary and which describes inertial motions (i.e., evolution absence forces). From generalized law, corresponding Hamilton's canonical equations theory (Hamilton-De Donder-Weyl equations) obtained simple procedure. It is shown that solutions equation also hold equations. However, unlike case, Newton determined different forces can define equal