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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
Creators:
CreatorsEmailORCID
Curiel, Erikerik@strangebeautiful.com
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 16:08
Last Modified: 25 May 2011 16:08
Item ID: 8625
URI: http://philsci-archive.pitt.edu/id/eprint/8625

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