Adapting the Euler-Lagrange equation to study one-dimensional motions under the action of a constant force

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.