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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| Дата: | 2003 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2003
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| Назва видання: | Нелінійні коливання |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/176161 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-176161 |
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irk-123456789-1761612021-02-04T01:29:58Z Determination of the boundaries between the domains of stability and instability for the Hill's equation Grebenikov, E.A. Prokopenya, A.N. 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 ). Проблема стабiльностi для рiвняння Хiлла, яке мiстить два параметри, вивчається за допомогою комп’ютерної системи M athematica. Знайдено характеристичну константу в термiнах ряду вiдносно степенiв малого параметра e. Показано, що областi стабiльностi i нестабiльностi знаходяться тiльки на площинi a − e мiж кривими a = a(e), що перетинають вiсь e = 0 в точках a = (2k − 1)²/4, k = 1, 2, 3 . . . . Знайдено вiдповiднi кривi як ряди за степенями e з точнiстю O(e⁶). 2003 Article 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. 1562-3076 http://dspace.nbuv.gov.ua/handle/123456789/176161 517.9 en Нелінійні коливання Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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 ). |
| format |
Article |
| author |
Grebenikov, E.A. Prokopenya, A.N. |
| spellingShingle |
Grebenikov, E.A. Prokopenya, A.N. Determination of the boundaries between the domains of stability and instability for the Hill's equation Нелінійні коливання |
| author_facet |
Grebenikov, E.A. Prokopenya, A.N. |
| author_sort |
Grebenikov, E.A. |
| title |
Determination of the boundaries between the domains of stability and instability for the Hill's equation |
| title_short |
Determination of the boundaries between the domains of stability and instability for the Hill's equation |
| title_full |
Determination of the boundaries between the domains of stability and instability for the Hill's equation |
| title_fullStr |
Determination of the boundaries between the domains of stability and instability for the Hill's equation |
| title_full_unstemmed |
Determination of the boundaries between the domains of stability and instability for the Hill's equation |
| title_sort |
determination of the boundaries between the domains of stability and instability for the hill's equation |
| publisher |
Інститут математики НАН України |
| publishDate |
2003 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/176161 |
| citation_txt |
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. |
| series |
Нелінійні коливання |
| work_keys_str_mv |
AT grebenikovea determinationoftheboundariesbetweenthedomainsofstabilityandinstabilityforthehillsequation AT prokopenyaan determinationoftheboundariesbetweenthedomainsofstabilityandinstabilityforthehillsequation |
| first_indexed |
2023-10-18T22:40:38Z |
| last_indexed |
2023-10-18T22:40:38Z |
| _version_ |
1796156142609498112 |