Gauge Functions for Forces and Nonlinearities in Classical Oscillators - Vestal, L. C.; Musielak, Z. E. (Journal of Applied Nonlinear Dynamics, 2026)
The abundance of gauge functions in dynamics is compelling because the total derivative of any scalar function can become a null Lagrangian, which makes the Euler-Lagrange equation identically zero. Thus, gauge functions have no direct effects on the resulting equations of motion. However, there is a special family of gauge functions that can be related directly to forces and nonlinearities in dynamical systems by using a method developed in this paper. To identify this special family, general 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 oscillators, including the Duffing oscillator, are presented, and the novel roles these functions play in classical dynamics are discussed.