Hamiltonian Dynamics
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Hamiltonian mechanics is a reformulation of classical mechanics that was introduced in 1833 by Irish mathematician William Rowan Hamilton.It arose from Lagrangian mechanics, a previous reformulation of classical mechanics introduced by Joseph Louis Lagrange in 1788, but can be formulated without recourse to Lagrangian mechanics using symplectic manifold|symplectic spaces (see #Mathematical formalism|Mathematical formalism, below). The Hamiltonian method differs from the Lagrangian method in that instead of expressing second-order differential constraints on an n-dimensional coordinate space (where n is the number of degrees of freedom (mechanics)|degrees of freedom of the system), it expresses first-order constraints on a 2n-dimensional phase space. As with Lagrangian mechanics, Hamilton's mathematical equation|equations provide a new and equivalent way of looking at Newtonian physics. Generally, these equations do not provide a more convenient way of solving a particular problem in...
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