The Concepts of Work and Potential Energy with Application to Continuous Systems

Abstract In this paper, we discuss how the principle of Galilean invariance, when applied to the conservation principle of total mechanical energy, imposes certain conditions on the choice of the particle system considered. First, changes in kinetic energy are not, generally, Galilean invariant, and second, potential energy must be defined for an interaction. We extend the definition of potential energy for interacting particles and show that total potential energy cannot be defined, in an invariant way, for arbitrary particle systems. These problems can only be solved if we consider closed systems. We also show how this approach is appropriate for applications of the work-energy theorem and the principle of energy conservation to continuous systems.