Training Manual . - Nizhny Novgorod: Nizhniy Novgorod State University . Foundation for Educational Electronic Publications, 2015. 60 s. Reg. Nom. 985. 15. 06. The general statement of the problem about angular motions of the viscoelastic body . is presented The relationship of symmetry of shape and elastic properties of bodies with their angular motions is analyzed. On specific systems, new phenomena in the dynamics of solids associated with their elastic and viscous properties are demonstrated. The results are used to interpret some features of the dynamics of the Earth. Designed for students of higher professional education, studying in the areas of training "Mechanics and mathematical modeling" .