Abstract
Hamiltonian systems form the most important class of ordinary differential equations in the context of ‘Geometric Numerical Integration’. An outstanding property of these systems is the symplecticity of the flow. As indicated in the following diagram, 
Hamiltonian theory operates in three different domains (equations of motion, partial differential equations and variational principles) which are all interconnected. Each of these viewpoints, which we will study one after the other, leads to the construction of methods preserving the symplecticity.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Joseph-Louis Lagrange, born: 25 January 1736 in Turin, Sardinia-Piedmont (now Italy), died: 10 April 1813 in Paris.
Feng Kang, born: 9 September 1920 in Nanjing (China), died: 17 August 1993 in Beijing; picture obtained from Yuming Shi with the help of Yifa Tang.
Carl Gustav Jacob Jacobi, born: 10 December 1804 in Potsdam (near Berlin), died: 18 February 1851 in Berlin.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hairer, E., Wanner, G., Lubich, C. (2002). Symplectic Integration of Hamiltonian Systems. In: Geometric Numerical Integration. Springer Series in Computational Mathematics, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05018-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-662-05018-7_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-05020-0
Online ISBN: 978-3-662-05018-7
eBook Packages: Springer Book Archive