Null Lagrangians and Gauge Functions in Dynamical Systems: Forces and Nonlinearities
Mathematical Physics
2022-10-18 v1 math.MP
Abstract
Among different Lagrangians, null Lagrangians are known for having identically zero the Euler-Lagrange equation and, therefore, they have no effects on the resulting equations of motion. However, there is a special family of null Lagrangians that can be used to convert linear and undriven equations of motion into nonlinear and driven ones. To identify this special family, general null Lagrangians and their gauge functions are constructed for second-order ordinary differential equations of motion describing one-dimensional dynamical systems. The gauge functions corresponding to forces and nonlinearities in a variety of known dynamical systems are presented and novel roles of these functions in dynamics are discussed.
Keywords
Cite
@article{arxiv.2210.08144,
title = {Null Lagrangians and Gauge Functions in Dynamical Systems: Forces and Nonlinearities},
author = {L. C. Vestal and Z. E. Musielak},
journal= {arXiv preprint arXiv:2210.08144},
year = {2022}
}