The Hamiltonian formulation is a reformulation of classical mechanics that describes a physical system in terms of its energy rather than forces. It uses the Hamiltonian function, typically denoted as H, which represents the total energy of the system, combining kinetic and potential energy. This approach is particularly useful for analyzing complex systems and is foundational in fields like quantum mechanics and statistical mechanics. In the Hamiltonian framework, the equations of motion are derived from Hamilton's equations, which relate the system's coordinates and momenta. This method allows for a more systematic treatment of dynamics, making it easier to apply to various problems, including those in field theory and chaos theory.