Tulczyjew triples in the constrained dynamics of strings
Abstract
We show that there exists a natural Tulczyjew triple in the dynamics of objects for which the standard (kinematic) configuration space TM is replaced with ∧n TM . In this framework, which is completely covariant, we derive geometrically 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.
- Publication:
-
Nuovo Cimento C Geophysics Space Physics C
- Pub Date:
- September 2016
- DOI:
- 10.1393/ncc/i2015-15162-6
- arXiv:
- arXiv:1509.07977
- Bibcode:
- 2016NCimC..38..162G
- Keywords:
-
- 02.40.-k;
- 11.10.Ef;
- Geometry differential geometry and topology;
- Lagrangian and Hamiltonian approach;
- Mathematical Physics;
- Mathematics - Differential Geometry;
- Primary: 70S05;
- 53C80 Secondary: 53D17;
- 58A20;
- 58A32;
- 70G45
- E-Print:
- 14 pages. arXiv admin note: text overlap with arXiv:1401.6970