On the construction of configuration spaces (Q1072742)

In a continuous body, i.e. a smooth manifold of dimension n, the manifold assigns to each point of the body a real tangent space. In continuum mechanics it is usually assumed that the body can be placed as a whole in an external translation space. In this paper it is assumed that each point is placed in its own reference space but not in the translation space. It is shown how the configuration of the body can be constructed from the set of all placements which has the structure of a Lie group.