arXiv subjects

L. C. Vestal

Publications and source records attributed to L. C. Vestal.

4 recordsLinked to original sources

arXiv2022

Null Lagrangians and Gauge Functions in Dynamical Systems: Forces and Nonlinearities

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.

math-ph↗

arXiv2022

Nonstandard Null Lagrangians and Gauge Functions and Dissipative Forces in Dynamics

Standard and non-standard Lagrangians that give the same equation of motion are significantly different in their forms, as the latter do not have terms that clearly discernable energy-like expressions. A special family of these Lagrangians are null Lagrangians and their gauge functions. It is shown that non-standard null Lagrangians and their gauge functions can be used to introduce dissipative forces to dynamical systems. With standard null Lagrangians being known for introducing non-dissipative forces, the presented results allow for a complete picture of novel roles played by null Lagrangians in introducing forces to dynamics. Applications of the results to Newton's laws are presented and their Galilean invariance is discussed.

math-ph↗

arXiv2021

Bateman Oscillators: Caldirola-Kanai and Null Lagrangians and Gauge Functions

The Lagrange formalism is developed for Bateman oscillators, which include both damped and amplified systems, and a novel method to derive the Caldirola-Kanai and null Lagrangians is presented. For the null Lagrangians, corresponding gauge functions are obtained. It is shown that the gauge functions can be used to convert the undriven Bateman oscillators into the driven ones. Applications of the obtained results to quantizatation of the Bateman oscillators are briefly discussed.

physics.class-ph↗

arXiv2020

Gauge Functions in Classical Mechanics: From Undriven to Driven Dynamical Systems

Novel gauge functions are introduced to non-relativistic classical mechanics and used to define forces. The obtained results show that the gauge functions directly affect the energy function and that they allow converting an undriven physical system into a driven one. This is a novel phenomenon in dynamics that resembles the role of gauges in quantum field theories.

math-ph↗