Oscillations and Dynamical Systems: Normalization Procedures and Averaging
- Lopatin, Alexey K.
The present lecture deals with the development of new normalization procedures and averaging algorithms in problems of nonlinear vibrations. Namely, the development of asymptotic methods of perturbation theory is considered, making wide use of group theoretical techniques. Various assumptions about specific group properties are investigated, and are shown to lead to modifications of existing methods, such as the Bogoliubov averaging method and the Poincaré-Birkhoff normal form, as well as to the formulation of new ones. The development of normalization techniques on Lie groups is also treated.