Motion of Spinning and Spinning Deviation Density Tensors in Riemannian Geometry

Abstract: Equations of motion of spinning density for extended objects, and corresponding deviation equations are derived. The problem of motion for a variable mass to 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, spinning density tensor can be expressed in terms of tetrad formalism of General Relativity to be regarded as a gauge theory of gravity. Equations of spinning and spinning deviation density tensors have been derived using a specific type of Bazanski Lagrangian is performed.