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

摘要

Discussed is mechanics of objects with internal degrees of freedom ingenerally non-Euclidean spaces. Geometric peculiarities of the model areinvestigated detailly. Discussed are also possible mechanical applications,e.g., in dynamics of structured continua, defect theory and in other fields ofmechanics of deformable bodies. Elaborated is a new method of analysis based onnon-holonomic frames. We compare our results and methods with those of otherauthors working in nonlinear dynamics (many of them refer to our papers [20],[21], [49], [50]). Simple examples of completely integerable models arepresented.