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Discussed is kinematics and dynamics of bodies with affine degrees offreedom, i.e., homogeneously deformable "gyroscopes". The special stress islaid on the status and physical justification of affine dynamical invariance.On the basis of classical Hamiltonian formalism the Schroedinger quantizationprocedure is performed. Some methods of the partial separation of variables,analytical treatment and search of rigorous solutions are developed. Thepossiblity of applications in theory of structured media, nanophysics, andmolecular physics is discussed.

Quantization of affine bodies. Theory and applications in mechanics of structured media