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.

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