Перегляд за автором "Lopatin, A.K."

Сортувати за: Порядок: Результатів:

  • Bogolyubov averaging and normalization procedures in nonlinear mechanics. I 
    Mitropolsky, Yu.A.; Lopatin, A.K. (Український математичний журнал, 1994)
    A new method of asymptotic analysis of nonlinear dynamical systems is developed with extensive use of group-theoretical methods. The technique of normalization, which is named an "asymptotic decomposition" by the authors, ...
  • Bogolyubov averaging and normalization procedures in nonlinear mechanics. II 
    Mitropolsky, Yu.A.; Lopatin, A.K. (Український математичний журнал, 1994)
    By using a new method suggested in the first part of the present work, we study systems which become linear in the zero approximation and have perturbations in the form of polynomials. This class of systems has numerous ...
  • Bogolyubov averaging and normalization procedures in nonlinear mechanics. III 
    Mitropolsky, Yu.A.; Lopatin, A.K. (Український математичний журнал, 1994)
    We describe the technique of normalization based on the method of asymptotic decomposition in the space of representation of a finite-dimensional Lie group. The main topics of the theory necessary for understanding the ...
  • Bogolyubov averaging and normalization procedures in nonlinear mechanics. IV 
    Lopatin, A.K.; Mitropolskiy, Yu.A. (Український математичний журнал, 1995)
    In this paper, we apply the theory developed in parts I-III to some classes of problems. We consider linear systems in zero approximation and investigate the problem of invariance of integral manifolds under perturbations. ...
  • Normalization and averaging on compact lie groups in nonlinear mechanics 
    Lopatin, A.K. (Український математичний журнал, 1997)
    We consider the method of normal forms, the Bogolyubov averaging method, and the method of asymptotic decomposition proposed by Yu. A. Mitropol’skii and the author of this paper. Under certain assumptions about group-theoretic ...