Dynamical and kinematical near homoaxial rotations suitable for representation of nonuniformly rotating stars with extended atmospheres

Abstract

In this paper, a nontrivial ‘velocity tensor’ is suitably defined to represent in the common frame the so-called ‘classes of dynamical and kinematical near homoaxial rotations’ of a deformable finite material continuum. These classes have simple and interesting physical interpretation, especially for treating of nonuniform rotation and its applications to astrophysics. Some important ‘subclasses’ and ‘derived classes’ (in the sense of related superclasses) are also discussed.

Two coordinate systems are further introduced, one of which rotates uniformly while the other rotates nonuniformly, the latter defined by means of a ‘generalized orthogonal coordinate transformation’. Suitable conditions are then given, asserting that the above systems are ‘preferred’ in the sense of preserving the motion of the continuum in its inertial class.

Finally, the required concepts of ‘homotropy’ and ‘distributivity’ are defined and the method, by which the established mathematical framework will be subsequently used in applications, is discussed.