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