Marsden, Jerrold E. and Ratiu, Tudor S. (2009) Mechanical Systems: Symmetry and Reduction. In: Encyclopedia of Complexity and Systems Science. Vol.6/F. Springer-Verlag , New York, pp. 5482-5510. ISBN 9780387758886 http://resolver.caltech.edu/CaltechAUTHORS:20101005-095157909
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Reduction theory is concerned with mechanical systems with symmetries. It constructs a lower dimensional reduced space in which associated conservation laws are taken out and symmetries are \factored out" and studies the relation between the dynamics of the given system with the dynamics on the reduced space. This subject is important in many areas, such as stability of relative equilibria, geometric phases and integrable systems.
|Item Type:||Book Section|
|Additional Information:||This version: September 30, 2007. This work summarizes the contributions of many people. We are especially grateful to Alan Weinstein, Victor Guillemin and Shlomo Sternberg for their incredible insights and work over the last few decades. We also thank Hernán Cendra and Darryl Holm, our collaborators on the Lagrangian context and Juan-Pablo Ortega, a longtime collaborator on Hamiltonian reduction and other projects; he along with Gerard Misiolek and Matt Perlmutter were our collaborators on [HStages], a key recent project that helped us pull many things together. We also thank many other colleagues for their input and invaluable support over the years; this includes Larry Bates, Tony Bloch, Marco Castrillón-López, Richard Cushman, Laszlo Fehér, Mark Gotay, John Harnad, Eva Kanso, Thomas Kappeler, P.S. Krishnaprasad, Naomi Leonard, Debra Lewis, James Montaldi, George Patrick, Mark Roberts, Miguel Rodríguez-Olmos, Steve Shkoller, Jędrzej Śniatycki, Leon Takhtajan, Karen Vogtmann, and Claudia Wulff.|
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|Deposited By:||Tony Diaz|
|Deposited On:||17 Nov 2010 00:17|
|Last Modified:||26 Dec 2012 12:30|
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