ON SOLVING INVERSE PROBLEMS OF DYNAMICS

Shalaginova Olga Borisovna, Stakhno Roman Evgenievich

The article presents an overview of inverse problems of dynamics that arise in the diagnosis of holonomic systems with lumped and distributed parameters under conditions of uncertainty, the formulation of inverse problems for non-holonomic systems, and their comparison with known inverse problems for holonomic systems. The problem of determining the type of mechanical system from the observed properties of motion is considered, as well as the identification of mechanical systems with the choice of the class of friction functions being sought and the description of classes of boundary conditions. It has been determined that statistical methods play a key role in identifying systems, as they allow data processing, taking into account random and systematic measurement errors, and also assessing the degree of uncertainty in model parameters. The use of statistical methods in identification allows for qualitative data analysis, establishing connections between variables, and estimating model parameters and their uncertainty. This helps create accurate and reliable mathematical models of systems, which in turn allows you to more effectively manage systems, make informed decisions and develop new technologies and modern mechanisms.

Keywords:Inverse problem of dynamics, differential equation, holonomic system, statistical method, oscillatory system.