Abstract
Abstract
The space of null Lagrangians is the least investigated territory in dynamics as these Lagrangians are identically sent to zero by their Euler–Lagrange operator, and thereby they are having no effects on equations of motion. A procedure that significantly generalizes the previous work, which appeared in (2022, Physica Scripta
97, 125213), is developed and used to construct null Lagrangians and then the corresponding non-standard Lagrangians, which represent a range of interesting dynamical systems. By using the generalized procedure, derivation of equations of motion for a harmonic oscillator as well as for the Bateman and Duffing oscillators is presented. The obtained results demonstrate a new role played by the null Lagrangians and their corresponding non-standard Lagrangians in describing linear and nonlinear, and dissipative and non-dissipative dynamical systems.
Subject
Condensed Matter Physics,Mathematical Physics,Atomic and Molecular Physics, and Optics
Cited by
2 articles.
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