Compatibility conditions and equations of motion in the linear micropolar theory of elasticity

The compatibility conditions in three-dimensional and two-dimensional linear micropolar elasticity theories in the distinct from forms spread in the scientific literature and analog of the formula of Cesaro are reduced. Besides formulas for definition of an antisymmetric part of strain tensor (stress tensor) through symmetric parts of strain tensor and bend-torsion tensor (stress tensor and couple-stress tensor) and an antisymmetric part of a bend-torsion tensor (couple-stress tensor) through an symmetric part of a bend-torsion tensor (couple-stress tensor) and also the integro-differential equations of motion of the micropolar theory elasticities concerning symmetric parts of stress tensor and couple-stress tensor are received.