Adapting the Euler–Lagrange equation to study one-dimensional motions under the action of a constant force. (6th December 2017)

• Record Type: Journal Article
• Authors: Dias, Clenilda F; Araújo, Maria A S; Carvalho-Santos, Vagson L
• Is Part Of: Physics education. Volume 53:Number 1(2018:Jan.)
• Publication Date: 2017-12-06
• Subjects: Physics -- Study and teaching (Secondary) -- Periodicals; 530.0712
• DOI: 10.1088/1361-6552/aa90de
• Languages: English
• ISSNs: 0031-9120

Abstract

Abstract: The Euler–Lagrange equations (ELE) are very important in the theoretical description of several physical systems. In this work we have used a simplified form of ELE to study one-dimensional motions under the action of a constant force. From the use of the definition of partial derivative, we have proposed two operators, here called mean delta operators, which may be used to solve the ELE in a simplest way. We have applied this simplification to solve three simple mechanical problems in which the particle is 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 introduce the lagrangian formalism in teaching classical mechanics in introductory physics courses.