The principal bundle structure of continuum mechanics
Abstract
In this paper it is shown that the structure of the configuration space of any continua is what is called in differential geometry a principle bundle. A principal bundle is a structure in which all points of the manifold (each configuration in this case) can be naturally projected to a manifold called the base manifold, which in our case represents pure deformations. All configurations projecting to the same point on the base manifold (same deformation) are called fibers. In this paper, it is shown that each of these fibers is then naturally isomorphic to the Lie group
- Publication:
-
Journal of Geometry and Physics
- Pub Date:
- June 2024
- DOI:
- 10.1016/j.geomphys.2024.105172
- arXiv:
- arXiv:2210.11537
- Bibcode:
- 2024JGP...20005172S
- Keywords:
-
- Continuum media;
- Principle bundle;
- Screw theory;
- Connection;
- Physics - Fluid Dynamics;
- Mathematical Physics