Bogolyubov averaging and normalization procedures in nonlinear mechanics. IV
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. Unlike nonlinear systems, linear ones have centralized systems, which are al...
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| Date: | 1995 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
1995
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| Series: | Український математичний журнал |
| Subjects: | |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Bogolyubov averaging and normalization procedures in nonlinear mechanics. IV / A.K. Lopatin, Yu.A. Mitropolskiy // Український математичний журнал. — 1995. — Т. 47, № 8. — С. 1044–1068. — Бібліогр.: 5 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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. Unlike nonlinear systems, linear ones have centralized systems, which are always decomposable. Moreover, restrictions connected with the impossibility of diagonalization of the coefficient matrix in zero approximation are removed. In conclusion, we apply the method of local asymptotic decomposition to some mechanical problems. |
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