Null Lagrangians: New Physics Hiding in Plain Sight

While standard Lagrangians have been widely studied and are known for describing the motion of a system, null Lagrangians are a special but lesser-known type of Lagrangian known for not contributing to the equation 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. In this presentation, I will discuss how null Lagrangians and their gauge functions are constructed for second-order ordinary differential equations of motion describing one-dimensional dynamical systems. Applications of the obtained results to selected dynamical systems are presented and discussed. The presented results illustrate the compelling role null Lagrangians play in introducing forces to dynamics.