ABSTRACT This project gives the discussion of Hamiltonian dynamics in relation to the calculus of variations. Hamiltonian dynamics defines the momenta as an independent parameter in the equations of motion. The equation of motion in a Hamiltonian dynamics system are of first order and define a 2n dimensional phase space of generalized coordinates and generalized momenta, for a Hamiltonian dynamical system the phase space is represented by generalized coordinates q, and generalized momenta p, which are canonical variables and independent of each other. Hamilton’s equation is equivalent to Hamilton’s principle of least action. Hamilton’s equation uses independent generalized coordinates, 𝑞 to drive equations of motion of a system. These equations of motion are either ordinary differential equations or partial differential equations. Application example of deriving ordinary differential equations of a system using Hamiltonian dynamics is given. 𝑖