Motion of test bodies with internal degrees of freedom in non-Euclidean spaces

Discussed is mechanics of objects with internal degrees of freedom in generally non-Euclidean spaces. Geometric peculiarities of the model are investigated in detail Discussed are also possible mechanical applications, e.g. in dynamics of structured continua, defect theory and in other fields of mechanics of deformable bodies. Elaborated is a new method of analysis based on nonholonomic frames. We compare our results and methods with those of other authors working in nonlinear dynamics. Simple examples are presented.