On symplectic reduction in classical mechanics

Abstract
This paper expounds the modern theory of symplectic reduction in finite-dimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether's theorem. It also illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. The exposition emphasises how the theory provides insights about the rotation group and the rigid body. The theory's device of quotienting a state space also casts light on philosophical issues about whether two apparently distinct but utterly indiscernible possibilities should be ruled to be one and the same. These issues are illustrated using ``relationist'' mechanics.
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Citations of this work BETA
Quantization as a Guide to Ontic Structure.P. Y. Thébault Karim - 2016 - British Journal for the Philosophy of Science 67 (1):89-114.
The Modal-Hamiltonian Interpretation and the Galilean Covariance of Quantum Mechanics.Olimpia Lombardi, Mario Castagnino & Juan Sebastián Ardenghi - 2010 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (2):93-103.
The Role of Symmetry in the Interpretation of Physical Theories.Adam Caulton - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52:153-162.
The Modal-Hamiltonian Interpretation and the Galilean Covariance of Quantum Mechanics.Olimpia Lombardi, Mario Castagnino & Juan Sebastián Ardenghi - 2010 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (2):93-103.

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