应用欧拉-拉格朗日方程研究常外力作用下action的一维运动
Adapting the Euler-Lagrange equation to study one-dimensional motions under the action of a constant force
摘要：
欧拉-拉格朗日方程在许多物理系统的理论描述中占有重要地位。在这项工作中，我们已经使用了一个简化的形式EL研究一维运动的作用下，一个恒定的力。利用偏导数的定义，我们提出了两个算子，这里称为\textit{mean delta operators}，这两个算子可以用来以最简单的方式求解EL。我们应用这种简化方法解决了引力场作用下的三个简单力学问题：自由降落、阿特伍德机和斜面。所提出的简化方法可用于在物理导论课程中引入拉格朗日形式讲授经典力学。
英文摘要：
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.
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