Gauge Functions in Classical Mechanics: From Undriven to Driven Dynamical Systems
@article{Musielak2020GaugeFI, title={Gauge Functions in Classical Mechanics: From Undriven to Driven Dynamical Systems}, author={Zdzislaw E. Musielak and L. C. Vestal and Bao Duy Tran and Timothy B. Watson}, journal={Physics}, year={2020}, volume={2}, pages={425-435} }
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 allow for 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.
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References
SHOWING 1-10 OF 37 REFERENCES
Gauge theory in Hamiltonian classical mechanics : The electromagnetic and gravitational fields
- Physics, Geology
- 1979
Gauge potentials are directly defined from Hamiltonian classical mechanics. Gauge transformations belong to canonical transformations and are determined by a first order development of generating…
Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories
- Physics
- 1997
We study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators…
Group-theoretical foundations of classical mechanics: The Lagrangian gauge problem
- Physics
- 1969
This paper is devoted to the study of the classical, single and free particle...
A direct approach to the construction of standard and non-standard Lagrangians for dissipative-like dynamical systems with variable coefficients
- Mathematics
- 2010
We present a direct approach to the construction of Lagrangians for a large class of one-dimensional dynamical systems with a simple dependence (monomial or polynomial) on the velocity. We rederive…
Gauge Field Theories
- Physics
- 1987
Preface Introduction 1. Classical fields, symmetries and their breaking 2. Path integral formulation of quantum field theory 3. Feynman rules for Yang-Mills theories 4. Introduction to the theory of…
Variational principles for nonpotential operators
- Mathematics
- 1994
One presents numerous approaches for the construction of variational principles for equations with operators which, in general, are nonpotential. One considers separately linear and nonlinear…
Gauge Field Theories
- Physics
- 1998
All the current successful theories of the fundamental forces start from the premise of invariance of the physical laws to certain coordinate-dependent transformations. In particular, the quantum…
Special Functions of Mathematical Physics: A Unified Lagrangian Formalism
- Physics, Mathematics
- 2020
Lagrangian formalism is established for differential equations with special functions of mathematical physics as solutions. Formalism is based on either standard or non-standard Lagrangians. This…
CORRIGENDUM: Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients
- Mathematics, Physics
- 2008
Dynamical systems described by equations of motion with the first-order time derivative (dissipative) terms of even and odd powers, and coefficients varying either in time or in space, are…