An algebraic approach for obtaining nilpotent normal forms in dimension 4
Autor: | Weiyi Zhang, K. Huseyin |
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Rok vydání: | 2000 |
Předmět: | |
Zdroj: | IMA Journal of Applied Mathematics. 64:109-123 |
ISSN: | 1464-3634 0272-4960 |
Popis: | In this paper, an algebraic approach is presented for determining the normal forms of four-dimensional systems with a nilpotent linear part. Certain transformations introduced in this case result in a simplified procedure for the calculation of normal forms. Thus, one does not need to solve a series of partial differential equations as usually required by the normal-form theory; indeed, algebraic calculations are sufficient. The approach can be applied to higher-order systems with a nilpotent linear part as well. To illustrate the new approach, five examples are presented. Normal forms and the associated coefficients of two physical systems, an electric network and a mechanical system, are fully analyzed. |
Databáze: | OpenAIRE |
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