  A method for constructing general null Lagrangians and their higher harmonics
is presented for dynamical systems with one degree of freedom. It is shown that
these Lagrangians can be used to obtain non-standard Lagrangians, which give
equations of motion for the law of inertia and some dissipative dynamical
systems. The necessary condition for deriving equations of motion by using null
Lagrangians is presented, and it is demonstrated that this condition plays the
same role for null Lagrangians as the Euler-Lagrange equation plays for
standard and non-standard Lagrangians. The obtained results and their
applications establish a novel role of null Lagrangians in classical dynamics.
