Article ID: CBB188856810

On the Structure of Classical Mechanics (2015)


The standard view is that the Lagrangian and Hamiltonian formulations of classical mechanics are theoretically equivalent. Jill North ([2009]), however, argues that they are not. In particular, she argues that the state-space of Hamiltonian mechanics has less structure than the state-space of Lagrangian mechanics. I will isolate two arguments that North puts forward for this conclusion and argue that neither yet succeeds. 1 Introduction 2 Hamiltonian State-space Has less Structure than Lagrangian State-space 2.1 Lagrangian state-space is metrical 2.2 Hamiltonian state-space is symplectic 2.3 Metric > symplectic 3 Hamiltonian State-space Does Not Have Less Structure than Lagrangian State-space 3.1 Lagrangian state-space has less than metric structure 3.1.1 A potential worry 3.1.2 General Lagrangians 3.2 Hamiltonian state-space (often) has more than symplectic structure 3.2.1 A dual structure on the Hamiltonian state-space 3.2.2 Simple Hamiltonians 3.3 Comparing Lagrangian and Hamiltonian structures 3.3.1 Counting mathematical structure 3.3.2 Symplectic and metric structure are incomparable 4 An Alternative Argument for LS 4.1 The argument for P3* 4.2 Symplectic manifold vs. tangent bundle structure 4.3 Trying to patch up the argument for P3* 5 Interpreting Mathematical Structure 5.1 State-space realism 5.2 Model isomorphism and theoretical equivalence 6 Conclusion

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Authors & Contributors
Nakane, Michiyo
Pulte, Helmut
Fraser, Craig G.
Drago, Antonino
Villone, Barbara
Frisch, Uriel
European Physical Journal H
Physics in Perspective
Transversal: International Journal for the Historiography of Science
Revue des Questions Scientifiques
Revue d'Histoire des Sciences
Llull: Revista de la Sociedad Española de Historia de las Ciencias y de las Técnicas
Wissenschaftliche Buchgesellschaft
Kluwer Academic
Edizioni ETS
University of Pittsburgh
Conservation of energy (physical concept)
History of philosophy of science
Lagrange, Joseph Louis
Hamilton, William Rowan
Jacobi, Karl Gustav Jakob
Helmholtz, Hermann Ludwig Ferdinand von
Euler, Leonhard
Hertz, Heinrich Rudolph
Time Periods
19th century
18th century
20th century
20th century, early
17th century
United States
Dublin (Ireland)
Trinity College Dublin
Université de Louvain
Académie des Sciences, Paris

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