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 |
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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 |

### Available Versions of this Item

- Classical Mechanics Is Lagrangian; It Is Not Hamiltonian; The Semantics of Physical Theory Is Not Semantical. (deposited 27 Sep 2009)
- Classical Mechanics Is Lagrangian; It Is Not Hamiltonian; The Semantics of Physical Theory Is Not Semantical. (deposited 04 Mar 2011 01:03)
- Classical Mechanics is Lagrangian; It Is Not Hamiltonian. (deposited 25 May 2011 12:08)
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- Classical Mechanics is Lagrangian; It Is Not Hamiltonian. (deposited 25 May 2011 12:08)

- Classical Mechanics Is Lagrangian; It Is Not Hamiltonian; The Semantics of Physical Theory Is Not Semantical. (deposited 04 Mar 2011 01:03)

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