OSCILLATION SHAPE CONTROL IN RESONANT SYSTEMS

A range of new perturbation theory problems is considered. A connectio n is established between different types of oscillation shape in confi guration space and manifolds defined in phase space. A construction of bases on these manifolds is given, so that each basis unit vector def ines one of the evolution forms of an oscillation shape under the infl uence of the perturbation. Algebraic properties of the local evolution basis are established. A classification of the perturbations is intro duced according to the nature of the evolution induced on the oscillat ion shape. The control and stability problems for the oscillation shap es are solved. Similar problems include, in particular, the problem of controlling waves in uniaxial and triaxial gyroscopes, based on the i nertia effect for elastic waves [1, 2].