Determination of the boundaries between the domains of stability and instability for the Hill's equation
Stability problem for the Hill’s equation containing two parameters is analyzed with computer algebra system M athematica. The characteristic constant is found as a series expansion in powers of a small parameter e. It has been shown that the domains of instability are located only between the c...
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| Date: | 2003 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2003
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| Series: | Нелінійні коливання |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/176161 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Determination of the boundaries between the domains of stability and instability for the Hill's equation / E.A. Grebenikov, A.N. Prokopenya // Нелінійні коливання. — 2003. — Т. 6, № 1. — С. 42-51. — Бібліогр.: 12 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | Stability problem for the Hill’s equation containing two parameters is analyzed with computer algebra
system M athematica. The characteristic constant is found as a series expansion in powers of a small
parameter e. It has been shown that the domains of instability are located only between the curves a = a(e)
on the a−e plane crossing the e = 0 axis at the points a = (2k−1)²/4, k = 1, 2, 3 . . . . The corresponding
curves are found as power series in e with accuracy O(e⁶ ). |
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