Hamiltonian mechanics | Wikipedia audio article
Channel: wikipedia tts
Date: 08/12/2018

This is an audio version of the Wikipedia Article:
Hamiltonian mechanics


00:00:41 1 Overview
00:02:35 1.1 Basic physical interpretation
00:04:08 1.2 Calculating a Hamiltonian from a Lagrangian
00:04:32 2 Deriving Hamilton's equations
00:15:30 3 As a reformulation of Lagrangian mechanics
00:23:17 4 Geometry of Hamiltonian systems
00:23:55 5 Generalization to quantum mechanics through Poisson bracket
00:25:49 6 Mathematical formalism
00:29:31 7 Riemannian manifolds
00:31:07 8 Sub-Riemannian manifolds
00:33:04 9 Poisson algebras
00:33:43 10 Charged particle in an electromagnetic field
00:37:11 11 Relativistic charged particle in an electromagnetic field
00:44:38 12 See also



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SUMMARY
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Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian 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 statistical mechanics and 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.