Method of integrodifferential relations and projection technique in control problems of elastic body motions

摘要

The possibility of reducing an initial-boundary value problem formulated initially in partial derivatives to a system of ordinary differential equations of small dimension is considered. The properties of various quadratic energy relations arising in different problems of mathematical physics are studied and discussed. As an example, integro-differential formulations of a control problem of elastic body motion are presented in the framework of the two-dimensional theory of elasticity. It is shown that in this case the control problem using semi-discrete approximations with polynomials as basis functions can be reduced to a system of ordinary differential equations. In conclusion, the results of numerical simulation are presented and discussed.