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On Symplectic Reduction in Classical Mechanics

Butterfield, Jeremy (2005) On Symplectic Reduction in Classical Mechanics. [Preprint]

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    Abstract

    This paper expounds the modern theory of symplectic reduction in finite-dimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether's theorem. It also illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. The exposition emphasises how the theory provides insights about the rotation group and the rigid body. The theory's device of quotienting a state space also casts light on philosophical issues about whether two apparently distinct but utterly indiscernible possibilities should be ruled to be one and the same. These issues are illustrated using ``relationist'' mechanics.


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    Item Type: Preprint
    Additional Information: This is a Chapter of the forthcoming North Holland `Handbook of Philosophy of Physics', edited by J. Earman and J. Butterfield
    Keywords: Hamiltonian mechanics; symmetry; reduction; conserved quantities; symplectic geometry; relationism
    Subjects: Specific Sciences > Physics > Classical Physics
    Depositing User: Jeremy Butterfield
    Date Deposited: 22 Jul 2005
    Last Modified: 07 Oct 2010 11:13
    Item ID: 2373
    URI: http://philsci-archive.pitt.edu/id/eprint/2373

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