Energy conservation is a deep principle that is obeyed by all of the fundamental forces of nature.
It puts stringent constraints on all systems, particularly systems that are ‘isolated,’ meaning that
no energy can enter or escape. Notwithstanding the success of the principle of stationary action, it
is fair to wonder to what extent physics can be formulated from the principle of stationary energy.
We show that if one interprets mechanical energy as a state function, then its stationarity leads to
a novel formulation of classical mechanics. However, unlike Lagrangian and Hamiltonian mechanics,
which deliver their state functions via algebraic proscriptions (i.e., the Lagrangian is always the
difference between a system’s kinetic and potential energies), this new formalism identifies its
state functions as the solutions to a differential equation. This is an important difference because
differential equations can generate more general solutions than algebraic recipes. When applied…