From the Cosserats mechanics backgrounds to modern field theory
Waldemar Dudda
Faculty of Technical Sciences, University of Warmia and Mazury in OlsztynJanusz Badur
Abstract
In the paper, yet weekly known, Cosserats’ original four concepts as follow: the four-time unification of rigid body dynamics, statics of flexible rods, statics of elastic surfaces and 3D deformable body dynamics; the intrinsic formulation based on the local, von Helmholtz symmetry group of monodromy; the invariance under the Euclidean group. The concept of a set of low-dimensional branes immersed into Euclidean space are revalorized and explained in terms of the modern gauge field theory and the extended strings theory. Additionally, some useful mathematical tools that connect the continuum mechanics and the classical field theory (for instance, the convective coordinates, von Mises’ “Motorrechnung”, the Grassmann extensions, Euclidean invariance, etc.) are involved in the historical explanation that how the ideas were developing themself.
Keywords:
Cosserats continuum, Darboux curvature vector, moving frame, Frenet trihedron, intrinsic coordinates, four-time operators, gauge symmetry flux conservation, gauge potentials, Mauer-Cartan structure equations, von Helmholtz symmetry group, Euclidean group of transformations, weak principle of momentum and angular momentum conservation, Euler laws of dynamics, Cauchy first and second lawsReferences
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Faculty of Technical Sciences, University of Warmia and Mazury in Olsztyn
