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It began with d'Alembert's principle. By analogy with Fermat's principle, which is the variational principle in geometric optics, Maupertuis' principle was discovered in classical mechanics.
Using generalized coordinates, we obtain Lagrange's equations. Using the Legendre transformation, we obtain
generalized momentum and the Hamiltonian. Hamilton's canonical equations provides integral, while Lagrange's equation provides differential equations. Finally we may derive the Hamilton-Jacobi equations. Theoretical physicsTheoretical physics attempts to understand the world by making a model of reality, used for rationalizing, explaining, predicting physical phenomena through a physical theory . There are three types of theories in physics; mainstream theories, proposed th Dynamical systems MechanicsMechanics ( Latin mechanicus from the Greek mechanikos "one skilled in machines") is a variety of specialised sciences pertaining to the functions and routine operations of machines, machine-like devices or objects. When preceded by a qualifier, mechanics