Applications in solution of physical problems by using Lagrange and Hamilton s equations for conservative systems

In this paper, Lagrange and Hamilton s equations for the conservative systems have been studied through the applications and solving some physical questions in Newton s field, electrical field, also of the plants moving within the sun s gravity field as well, the solving also have been compared and found all identical , and extraction of the potential energy of conservative force. But dealing with Hamilton s equations is easier because they are from the first order; therefore, we are dealing with the scalar quantities and not dealing with vector once as in Newton s mechanics.