large particles - classical mechanics
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Lagrangian mechanics is a re-formulation of classical mechanics using Hamilton's principle of stationary action . [ 1 ] Lagrangian mechanics applies to systems whether or not they conserve energy or momentum, and it provides conditions under which energy and/or momentum are conserved. [ 2 ] It was introduced by the Italian-French mathematician Joseph-Louis Lagrange in 1788.
Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics which predicts the same outcomes as classical mechanics. It uses a different mathematical formalism, providing a more abstract understanding of the theory. Historically, it was an important reformulation of classical mechanics, which later contributed to the formulation of the quantum mechanics . Hamiltonian mechanics was first formulated by William Rowan Hamilton in 1833, starting from Lagrangian mechanics , a previous reformulation of classical mechanics introduced by Joseph Louis Lagrange in 1788.