Discussion of systems with constraints that cannot be expressed purely in terms of coordinates, known as nonholonomic systems.

Introduction of the Legendre transformation leading to the Hamiltonian, followed by the derivation of Hamilton's canonical equations of motion.

Analysis of the Hamiltonian function, its interpretation as the total energy of the system in many cases, and its role in the Hamiltonian formalism.

Derivation of Hamilton’s equations of motion from a variational principle, introduction of Routh’s procedure, Δ-variation, and the principle of least action.