Quadratic and Rigidity Mappings

As opposed to the case of functions, the quadratic mappings from $\mathbb R^l$ to$\mathcal R^r$ for not too small $l$ and $r$ are studied immeasurably worse than the linear ones. Likewise, little is known about the class of quadratic mappings whose coordinate functions are the squares of certain pairwise distances between points thrown into a Euclidean space (this class is important for the Euclidean geometry). Such mappings are called rigidity mappings in this paper. The geometric properties of rigidity mappings are discussed. The tangent cone of a mapping and the notions of stability and rigidity order of a point under a mapping, which arise in the theory of hinged mechanisms, are studied from general positions.