On motions as rigid as possible. II (Q1083878)

[For part I see the author, ibid. 60-68 (1983; Zbl 0591.70001.] This paper is the continuation of a previous one, where the notion of as rigid as possible infinitesimal motion on a Riemannian manifold was introduced. Here as Euclidean as possible orthonormal frames are defined by minimizing a certain functional. Under regularity conditions of the domain, it is proved their existence and uniqueness up to a constant orthogonal transformation. Then, this result is used to obtain consequences for as rigid as possible infinitesimal motions. In particular it is shown that these motions are as many as the classical ones.