  The Euler-Lagrange equations (EL) are very important in the theoretical
description of several physical systems. In this work we have used a simplified
form of EL to study one-dimensional motions under the action of a constant
force. From using the definition of partial derivative, we have proposed two
operators, here called \textit{mean delta operators}, which may be used to
solve the EL in a simplest way. We have applied this simplification to solve
three simple mechanical problems under the action of the gravitational field: a
free fall body, the Atwood's machine and the inclined plan. The proposed
simplification can be used to introducing the lagrangian formalism to teach
classical mechanics in introductory physics courses.
