When reading about the Calculus of Variation and Hamilton's principle I come across quotes like this
Hamilton's principle states that the differential equations of motion for any physical system can be re-formulated as an equivalent integral equation. Thus, there are two distinct approaches for formulating dynamical models.
This has me curious. What systems submit to this transformation from differential equations to functionals? Can the calculus of variations be applied to any differential equation, or are there restrictions? What is special about "physical systems" which permit this sort of manipulation?