Physics – Mathematical Physics
Scientific paper
2010-10-16
Mathematical Methods in the Applied Sciences, vol. 34, 2011, pp. 1512-1540
Physics
Mathematical Physics
50 pages, 4 figures
Scientific paper
10.1002/mma.1462
In the present paper we investigate the mechanics of systems of affinely-rigid bodies, i.e., bodies rigid in the sense of affine geometry. Certain physical applications are possible in modelling of molecular crystals, granular media, and other physical objects. Particularly interesting are dynamical models invariant under the group underlying geometry of degrees of freedom. In contrary to the single body case there exist nontrivial potentials invariant under this group (left and right acting). The concept of relative (mutual) deformation tensors of pairs of affine bodies is discussed. Scalar invariants built of such tensors are constructed. There is an essential novelty in comparison to deformation scalars of single affine bodies, i.e., there exist affinely-invariant scalars of mutual deformations. Hence, the hierarchy of interaction models according to their invariance group, from Euclidean to affine ones, can be considered.
Go\lubowska B.
Kovalchuk Vasyl
Martens Agnieszka
Rożko Ewa Eliza
S\lawianowski Jan J.
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