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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).

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