On the stability and integration of Hamilton-Poisson systems on so(3)*_
We consider inhomogeneous quadratic Hamilton-Poisson systems on the Lie-Poisson space so(3)*_. There are nine such systems up to affine equivalence. We investigate the stability nature of the equilibria for each of these systems. For a subclass of systems, we find explicit expressions for the inte...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
2016-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2016(1-2)/1-42.pdf |
| _version_ | 1828943009847181312 |
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| author | R. M. Adams R. Biggs W. Holderbaum C. C. Remsing |
| author_facet | R. M. Adams R. Biggs W. Holderbaum C. C. Remsing |
| author_sort | R. M. Adams |
| collection | DOAJ |
| description | We consider inhomogeneous quadratic Hamilton-Poisson systems on the Lie-Poisson space so(3)*_. There are nine such systems up to affine equivalence. We
investigate the stability nature of the equilibria for each of these systems. For a subclass
of systems, we find explicit expressions for the integral curves in terms of Jacobi elliptic
functions. |
| first_indexed | 2024-12-14T04:06:03Z |
| format | Article |
| id | doaj.art-81ba895e7e054ecda2a4cb8e1fed9681 |
| institution | Directory Open Access Journal |
| issn | 1120-7183 2532-3350 |
| language | English |
| last_indexed | 2024-12-14T04:06:03Z |
| publishDate | 2016-01-01 |
| publisher | Sapienza Università Editrice |
| record_format | Article |
| series | Rendiconti di Matematica e delle Sue Applicazioni |
| spelling | doaj.art-81ba895e7e054ecda2a4cb8e1fed96812022-12-21T23:17:49ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33502016-01-01371-2142On the stability and integration of Hamilton-Poisson systems on so(3)*_R. M. Adams0R. Biggs1W. Holderbaum2C. C. Remsing3Department of Mathematics, Rhodes UniversityDepartment of Mathematics, Rhodes UniversitySchool of Systems Engineering, University of ReadingDepartment of Mathematics, Rhodes UniversityWe consider inhomogeneous quadratic Hamilton-Poisson systems on the Lie-Poisson space so(3)*_. There are nine such systems up to affine equivalence. We investigate the stability nature of the equilibria for each of these systems. For a subclass of systems, we find explicit expressions for the integral curves in terms of Jacobi elliptic functions.https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2016(1-2)/1-42.pdfhamilton-poisson systemlie-poisson structurelyapunov stabilityenergy-casimir methodjacobi elliptic function |
| spellingShingle | R. M. Adams R. Biggs W. Holderbaum C. C. Remsing On the stability and integration of Hamilton-Poisson systems on so(3)*_ Rendiconti di Matematica e delle Sue Applicazioni hamilton-poisson system lie-poisson structure lyapunov stability energy-casimir method jacobi elliptic function |
| title | On the stability and integration of Hamilton-Poisson systems on so(3)*_ |
| title_full | On the stability and integration of Hamilton-Poisson systems on so(3)*_ |
| title_fullStr | On the stability and integration of Hamilton-Poisson systems on so(3)*_ |
| title_full_unstemmed | On the stability and integration of Hamilton-Poisson systems on so(3)*_ |
| title_short | On the stability and integration of Hamilton-Poisson systems on so(3)*_ |
| title_sort | on the stability and integration of hamilton poisson systems on so 3 |
| topic | hamilton-poisson system lie-poisson structure lyapunov stability energy-casimir method jacobi elliptic function |
| url | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2016(1-2)/1-42.pdf |
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