Abstract
In this chapter, we will briefly recall the Hamiltonian formulation of classical mechanics, focusing in particular on its algebraic aspects. In this framework, a classical system will be described by a commutative algebra of functions (classical observables) with the Poisson bracket as a Lie bracket.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
R. Abraham, J.E. Marsden, Foundations of Mechanics, 2nd edn. (AMS Chelsea Publications, New York, 1980)
V.I. Arnold, Mathematical Methods of Classical Mechanics, 2nd edn. (Springer, New York, 1997)
A. Cannas da Silva, A. Weinstein, Geometric Models for Noncommutative Algebras, Berkeley Mathematics Lecture Notes series (AMS, Providence, 1999)
B. Casselman, Variations on a theorem of Émile Borel. Available on Casselman’s webpage http://www.math.ubc.ca/cass/research/pdf/Emile.pdf (2012)
L. Hörmander, The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis (Springer, Berlin, 1990)
J.E. Marsden, Introduction to Mechanics and Symmetry, vol. 17 (Springer, New York, 1999)
J.M. Ruiz, The Basic Theory of Power Series, Advanced Lectures in Mathematics (Vieweg, Braunschweig, 1993)
I. Vaisman, Lectures on the Geometry of Poisson Manifolds (Birkhäuser, Berlin, 1994)
S. Waldmann, Poisson-Geometrie und Deformationsquantisierung: Eine Einführung (Springer, Berlin, 2007)
H.S. Wilf, Generatingfunctionology, 3rd edn. (CRC Press, Natick, 2005)
N.T. Zung, J-P. Dufour, Poisson Structures and Their Normal Forms (Springer, Berlin, 2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 The Author(s)
About this chapter
Cite this chapter
Esposito, C. (2015). Classical Mechanics and Poisson Structures. In: Formality Theory. SpringerBriefs in Mathematical Physics, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-09290-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-09290-4_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09289-8
Online ISBN: 978-3-319-09290-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)