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arXiv · 1509.07977

Tulczyjew triples in the constrained dynamics of strings

Janusz Grabowski·Katarzyna Grabowska·Pawel Urbanski
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Abstract

We show that there exists a natural Tulczyjew triple in the dynamics of objects for which the standard kinematic configuration space $TM$, i.e. the tangent bundle, is replaced with its $n$-th exterior power, i.e. the bundle of tangent $n$-vectors. In this framework, which is fully covariant, we geometrically derive phase equations, as well as Euler-Lagrange equations, including nonholonomic constraints into the picture. Dynamics of strings and a constrained Plateau problem in statics are particular cases of this framework.

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Janusz Grabowski, Katarzyna Grabowska, Pawel Urbanski. 2015-09-26. Tulczyjew triples in the constrained dynamics of strings. https://doi.org/10.1393/ncc%2Fi2015-15162-6

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