Linear frames in manifolds, Riemannian structures and description of internal degrees of freedom.
The author first reviews the geometry of frame bundle of a manifold. Then he discusses a continuum mechanical interpretation of the frames as internal degrees of freedom (leading to an affinely rigid body in his terminology). This interpretation requires a metric on the frame bundle, and a number of different possibilities for natural derivation of such a metric from the geometry of the base manifold are considered. Finally, the corresponding Hamiltonian equations of motion are derived.
scientific article; zbMATH DE number 2084219
scientific article