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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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    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: Dr. Erik Curiel
    Date Deposited: 25 May 2011 12:08
    Last Modified: 25 May 2011 12:08
    Item ID: 8625

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