On Symmetry and Conserved Quantities in Classical Mechanics

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dc.creatorButterfield, Jeremy
dc.date2005-07-27
dc.date.accessioned2026-07-07T05:55:35Z
dc.date.available2026-07-07T05:55:35Z
dc.descriptionThis paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. I emphasise that, for both frameworks, the theorem is underpinned by the idea of cyclic coordinates; and that the Hamiltonian theorem is more powerful. The Lagrangian theorem's main ``ingredient'', apart from cyclic coordinates, is the rectification of vector fields afforded by the local existence and uniqueness of solutions to ordinary differential equations. For the Hamiltonian theorem, the main extra ingredients are the asymmetry of the Poisson bracket, and the fact that a vector field generates canonical transformations iff it is Hamiltonian.
dc.description60 pages, latex; forthcoming in a Festschrift for Jeffrey Bub, ed. W. Demopoulos and I. Pitowsky, to be published by Kluwer
dc.identifierhttps://arxiv.org/abs/physics/0507192
dc.identifierhttp://arxiv.org/abs/physics/0507192
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/87290
dc.subjectClassical Physics
dc.subjectHistory and Philosophy of Physics
dc.subjectPopular Physics
dc.titleOn Symmetry and Conserved Quantities in Classical Mechanics
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