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http://dspace.mediu.edu.my:8181/xmlui/handle/10261/2274| Title: | Symmetry aspects of nonholonomic field theories |
| Publisher: | Institute of Physics Publishing |
| Description: | The developments in this paper are concerned with nonholonomic field theories in the presence of symmetries. Having previously treated the case of vertical symmetries, we now deal with the case where the symmetry action can also have a horizontal component. As a first step in this direction, we derive a new and convenient form of the field equations of a nonholonomic field theory. Nonholonomic symmetries are then introduced as symmetry generators whose virtual work is zero along the constraint submanifold, and we show that for every such symmetry, there exists a so-called momentum equation, describing the evolution of the associated component of the momentum map. Keeping up with
the underlying geometric philosophy, a small modification of the derivation of the
momentum lemma allows us to treat also generalized nonholonomic symmetries, which are vector fields along a projection. Such symmetries arise for example in practical examples of nonholonomic field theories such as the Cosserat rod, for which we recover both energy conservation (a previously known result), as well
as a modified conservation law associated with spatial translations. Peer reviewed |
| URI: | http://dspace.mediu.edu.my:8181/xmlui/handle/10261/2274 |
| Other Identifiers: | Journal of Physics A: Mathematical and Theoretical, 2008 1751-8121 http://hdl.handle.net/10261/2274 |
| Appears in Collections: | Digital Csic |
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