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Bubnov-Galerkin method in problems of the control of vibrating mechanical systems with distributed parameters. (English. Russian original) Zbl 0707.70026
Sov. Phys., Dokl. 35, No. 5, 439-441 (1990); translation from Dokl. Akad. Nauk SSSR 312, No. 2, 294-298 (1990).
Summary: The Ritz method, the method of finite elements, and the Bubnov-Galerkin method are used to solve many problems of mechanics for a finite- dimensional approximation of systems with distributed parameters. The first two of these methods may be thought of as special cases of the Bubnov-Galerkin method.
Recent years have seen considerable interest in a new class of problems: controlling distributed mechanical systems. In the present paper we formulate the Bubnov-Galerkin method of the finite-dimensional approximation of a mechanical system to be controlled, and we study the convergence of this method for certain problems (the convergence of transfer functions).

70J35 Forced motions in linear vibration theory
74H45 Vibrations in dynamical problems in solid mechanics