On rigid displacements and their relation to the infinitesimal rigid displacement lemma in three-dimensional elasticity

Abstract

Let Ω be an open connected subset of R 3 and let Θ be an immersion from Ω into R 3 . It is established that the set formed by all rigid displacements of the open set Θ(Ω) is a submanifold of dimension 6 and of class C ∞ of the space H 1(Ω) . It is also shown that the infinitesimal rigid displacements of the same set Θ(Ω) span the tangent space at the origin to this submanifold. To cite this article: P.G. Ciarlet, C. Mardare, C. R. Acad. Sci. Paris, Ser. I 336 (2003).