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Classical Mechanics is Lagrangian; It Is Not Hamiltonian

Curiel, Erik (2011) Classical Mechanics is Lagrangian; It Is Not Hamiltonian. [Preprint]

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    Abstract

    One can (for the most part) formulate a model of a classical system in either the Lagrangian or the Hamiltonian framework. Though it is often thought that those two formulations are equivalent in all important ways, this is not true: the underlying geometrical structures one uses to formulate each theory are not isomorphic. This raises the question whether one of the two is a more natural framework for the representation of classical systems. In the event, the answer is yes: I state and sketch proofs of two technical results, inspired by simple physical arguments about the generic properties of classical systems, to the effect that, in a precise sense, classical systems evince exactly the geometric structure Lagrangian mechanics provides for the representation of systems, and none that Hamiltonian mechanics does. The argument not only clarifies the conceptual structure of the two systems of mechanics, their relations to each other, and their respective mechanisms for representing physical systems. It also shows why naively structural approaches to the representational content of physical theories cannot work.


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    Item Type: Preprint
    Keywords: classical mechanics; Lagrangian mechanics; Hamiltonian mechanics; scientific theories; structuralism
    Subjects: Specific Sciences > Physics > Classical Physics
    General Issues > Structure of Theories
    Depositing User: Erik Curiel
    Date Deposited: 25 May 2011 12:08
    Last Modified: 25 May 2011 12:08
    Item ID: 8625
    URI: http://philsci-archive.pitt.edu/id/eprint/8625

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