UDC 531.011+621.8.031

Invited Paper

Kazan Aviation Institute, Adamuck, 4-6, Kazan-15, 420015, RUSSIA

e-mail: Lyudmila.Kuzmina@ksu.ru

The research subject is complex large-scale systems, for which the original mathematical model, adequate real object, is extremely complex. The principal tasks are the elaborating universal methods of modelling; the constructing correct simplified models; the rigorous substantiating these reduced models in dynamics; the estimating errors and admissible parameters domains under using these reduced models (with keeping of qualitative equivalence).

Suggested method is combining the stability theory and perturbations theory methods based on two postulates (stability and singularity ones). It allows to work out the effective manners of rigorous analysis with general methodology of constructing simplified models and their analysing; with dividing of original problem on separate particular ones; with decomposing of original model and its dynamic characteristics; with building shortened models hierarchy; with revealing essential variables and freedom degrees. Besides the elaborated approach is extending the traditional statements of stability problems and perturbations theory, with the treating modelling problem as stability problem (in specific sense) under singular perturbations, with the extension of N.G.Chetayev's, K. P. Persidskiy ideas. Moreover the research results will allow to come nearer to fundamental modelling problem in complex systems dynamics. This problem is concerned with reduction principle in general qualitative analysis and with singularity problem in Mechanics. The results allow to get the developing theory of approximate methods for rigorous analysis; to give substantiation of approximate theories and models in Mechanics (both for traditional ones, well-known in engineering practice, and for new models, that are constructed by this developed method; including non-Newton models of Mechanics).