Motion of Spinning and Spinning Deviation in Riemannian Geometry

Equations of motion of spinning density for extended objects and tthe corresponding deviation equations are derived. The problem of motion for a variable mass of a spinning extended object is obtained. Spinning fluids may be considered as a special case to express the motion of spinning density for extended objects. Meanwhile, the spinning density tensor can be expressed in terms of the tetrad formalism of general relativity to be regarded as a gauge theory of gravity. The equations of spinning and spinning deviation density tensors have been derived using a specific type of Bazanski Lagrangian.