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.