Isolated systems and their symmetries, part I: General framework and particle-mechanics examples

Physical theories, for the most part, should be understood as modelling isolated subsystems of a larger universe; doing so, among other benefits, greatly clarifies the interpretation of the dynamical symmetries of those theories. I provide a detailed framework for analysing the subsystem structure of physical theories and applying it to the interpretation of their symmetries: the core concept is subsystem recursivity, whereby interpretative conclusions about a sector of a theory can be deduced from considering subsystems of other models of the same theory. I illustrate the framework by extensive examples from nonrelativistic particle mechanics, and in particular from Newtonian theories of gravity. A sequel to the paper will apply the framework to the local and global symmetries of classical field theory.