Abstract This project gives the discussion of Hamilton’s principle in relation to the calculus of variations. The principle states that “The motion of the system from time to time is such that the time integral of the Lagrangian is zero or Of all the possible paths along which a dynamical system can move from one point to another within a specific time interval, the actual path followed is that which minimizes the time integral of the difference between the kinetic and potential energies.” Hamilton’s principle is equivalent to Lagrange’s equation and Hamilton’s principle (least action principle) is also equivalent to Hamilton’s equations. The principle uses independent generalized coordinates, to drive equations of motion of a system. These equations of motion are either ordinary differential equations or partial differential equations.In the 3rd chapter of this project, application example of deriving partial differential equation of a system using Hamilton’s principle is given and an example of deriving ordinary differential equations of a system is also given.