General null Lagrangians and their novel role in classical dynamics. (1st December 2022)

• Record Type: Journal Article
• Authors: Das, R; Musielak, Z E
• Is Part Of: Physica scripta. Volume 97:Number 12(2022)
• Publication Date: 2022-12-01
• Subjects: classical dynamics -- null lagrangians -- equations of motion -- dissipative systems -- lagrangian formalism; Physics -- Periodicals; 530.05
• DOI: 10.1088/1402-4896/aca2fe
• Languages: English
• ISSNs: 0031-8949

Abstract

Abstract: 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.