Abstract
In this chapter we show how to obtain conserved quantities for Lagrangian and Hamiltonian systems with symmetries. This is done using the concept of a momentum mapping, which is a geometric generalization of the classical linear and angular momentum. This concept is more than a mathematical reformulation of a concept that simply describes the well-known Noether theorem. Rather, it is a rich concept that is ubiquitous in the modern developments of geometric mechanics. It has led to surprising insights into many areas of mechanics and geometry.
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© 1999 Springer Science+Business Media New York
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Marsden, J.E., Ratiu, T.S. (1999). Momentum Maps. In: Introduction to Mechanics and Symmetry. Texts in Applied Mathematics, vol 17. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21792-5_11
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DOI: https://doi.org/10.1007/978-0-387-21792-5_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3143-6
Online ISBN: 978-0-387-21792-5
eBook Packages: Springer Book Archive