Correspondence between Hamiltonian and Lagrangian Mechanics

In this paper, the most important results concerning the correspondence between the basic concepts of Hamiltonian mechanics and Lagrangian mechanics has been collected and expressed. These consequences include the mutual relation between Hamiltonian vector fields and Lagrangian vector fields, the mutual relation between integral curves of them, base integral curves of them. Also, representing the bijective correspondence between Lagrange equations and Hamiltonian equations, the feasibility of reconstruction Lagrangian from Hamiltonian, the feasibility of reconstruction Hamiltonian from Lagrangian are the other outcomes of this study.