Bogolyubov averaging and normalization procedures in nonlinear mechanics. III
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 method are outlined. Models based on the Van der Pol equation are investigated by...
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| Дата: | 1994 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1994
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5574 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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 method are outlined. Models based on the Van der Pol equation are investigated by the method of asymptotic decomposition in the space of homogeneous polynomials (the space of representation of a general linear group in a plane) and in the space of representation of a rotation group on a plane (ordinary Fourier series). The comparison made shows a dramatic decrease in the necessary algebraic manipulations in the second case. We also discuss other details of the technique of normalization based on the method of asymptotic decomposition. |
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