Article ID: CBB188856810

On the Structure of Classical Mechanics (2015)

unapi

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

...More
Citation URI
https://data.isiscb.org/isis/citation/CBB188856810/

Similar Citations

Article Gallavotti, Giovanni; (2013)
Aspects of Lagrange's Mechanics and their Legacy (/isis/citation/CBB001320790/)

Article Craig Fraser; Michiyo Nakane; (2023)
Canonical transformations from Jacobi to Whittaker (/isis/citation/CBB563006808/)

Chapter Antonino Drago; (2009)
Lagrange's Arguing in Mecanique Analytique (/isis/citation/CBB618628082/)

Thesis Hepburn, Brian S.; (2007)
Equilibrium and Explanation in 18th-Century Mechanics (/isis/citation/CBB001560501/)

Book Capecchi, Danilo; Drago, Antonino; (2005)
Lagrange e la storia della meccanica (/isis/citation/CBB000740070/)

Article Nakane, Michiyo; Fraser, Craig G.; (2002)
The Early History of Hamilton-Jacobi Dynamics, 1834--1837 (/isis/citation/CBB000300291/)

Article O'Connor, Thomas C.; (2014)
Daedalus in Dublin: A Physicist's Labyrinth (/isis/citation/CBB001421019/)

Article Frisch, Uriel; Villone, Barbara; (2014)
Cauchy's Almost Forgotten Lagrangian Formulation of the Euler Equation for 3D Incompressible Flow (/isis/citation/CBB001421685/)

Book Marco Panza; (2021)
Modes de l’analyse et formes de la géométrie (/isis/citation/CBB887755156/)

Chapter Patrizia Trovalusci; Giuseppe Ruta; Danilo Capecchi; (2009)
Il modello molecolare di Voigt (/isis/citation/CBB926157626/)

Article Coelho, Ricardo Lopes; (2013)
On Hertz’s Principles of Mechanics (/isis/citation/CBB589146351/)

Article Joshua Eisenthal; (2021)
Hertz's Mechanics and a unitary notion of force (/isis/citation/CBB462268539/)

Article Olivier Darrigol; (2020)
Deducing Newton’s second law from relativity principles: A forgotten history (/isis/citation/CBB773667166/)

Chapter Stefano Bordoni; (2009)
Discrete Models for Electromagnetic Radiation: J.J. Thomson and Einstein (/isis/citation/CBB519434910/)

Authors & Contributors
Nakane, Michiyo
Fraser, Craig G.
Drago, Antonino
Capecchi, Danilo
Kenichi Natsume
Joshua Eisenthal
Concepts
Mechanics
Physics
Mathematics
Motion (physical)
Logic
Chemistry
Time Periods
19th century
18th century
20th century
Early modern
20th century, early
Places
Europe
Great Britain
Dublin (Ireland)
France
Institutions
Trinity College Dublin
Académie des Sciences, Paris
Comments

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment