Hamiltonian mechanics

Classical hamiltonian mechanics is also known as hamiltonian mechanics. William hamilton first formulated a new mechanics which is now called Hamiltonian mechanics , starting from Lagrangian mechanics, a previous reformulation of classical mechanics introduced by Joseph Louis Lagrange in 1788. In Newtonian mechanics, the time evolution is obtained by computing the total force being exerted on each particle of the system, and from Newton's second law, the time-evolutions of both position and velocity are computed. In contrast, in Hamiltonian mechanics, the time evolution is obtained by computing the Hamiltonian of the system in the generalized coordinates and inserting it in the Hamilton's equations. Hamiltonian and Lagrangan are denoted by H and L which represent energy of a physical system. Hamiltonian H is related to Lagrangian L by certain relation, which are both reformulation of classical mechanics with more flexibility. Hamiltonian is a function of generalized coordinates like position q, momentum p and time t. It is the total energy of a system, which is algebric sum of potential and kinetic energy.

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