The variational theory of an ideal spinning fluid is developed. This is described by original Weyssenhoff-Raabe tensors of spin and energy-momentum. Both neutral and charged fluids are considered, and the equations of motion and conservation laws for the Weyssenhoff neutral fluid in the Riemann-Cartan spacetime are discussed. The results are applied to the study of cosmological models with rotation, shear and expansion in the framework of the Einstein-Cartan theory of gravity.
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Obukhov et al. (1987) studied this question.
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