Collective Heavy Top Dynamics
We construct a Poisson map M: T*C² → se(3)* with respect to the canonical Poisson bracket on T*C² ≅ T*ℝ⁴ and the (−)-Lie-Poisson bracket on the dual se(3)* of the Lie algebra of the special Euclidean group SE(3). The essential part of this map is the momentum map associated with the cotangent lift o...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2019 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2019
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210305 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Collective Heavy Top Dynamics / T. Ohsawa // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 17 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-210305 |
|---|---|
| record_format |
dspace |
| spelling |
Ohsawa, T. 2025-12-05T09:29:54Z 2019 Collective Heavy Top Dynamics / T. Ohsawa // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 17 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37J15; 37M15; 53D20; 70E17; 70E40; 70H05; 70H06 arXiv: 1907.07819 https://nasplib.isofts.kiev.ua/handle/123456789/210305 https://doi.org/10.3842/SIGMA.2019.083 We construct a Poisson map M: T*C² → se(3)* with respect to the canonical Poisson bracket on T*C² ≅ T*ℝ⁴ and the (−)-Lie-Poisson bracket on the dual se(3)* of the Lie algebra of the special Euclidean group SE(3). The essential part of this map is the momentum map associated with the cotangent lift of the natural right action of the semidirect product Lie group SU(2)⋉C² on C². This Poisson map gives rise to a canonical Hamiltonian system on T*C² whose solutions are mapped by M to solutions of the heavy top equations. We show that the Casimirs of the heavy top dynamics and the additional conserved quantity of the Lagrange top correspond to the Noether conserved quantities associated with certain symmetries of the canonical Hamiltonian system. We also construct a Lie-Poisson integrator for the heavy top dynamics by combining the Poisson map M with a simple symplectic integrator, and demonstrate that the integrator exhibits either exact or near conservation of the conserved quantities of the Kovalevskaya top. I would like to thank the referees for their helpful comments and suggestions. This work was partially supported by NSF grant CMMI-1824798. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Collective Heavy Top Dynamics Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Collective Heavy Top Dynamics |
| spellingShingle |
Collective Heavy Top Dynamics Ohsawa, T. |
| title_short |
Collective Heavy Top Dynamics |
| title_full |
Collective Heavy Top Dynamics |
| title_fullStr |
Collective Heavy Top Dynamics |
| title_full_unstemmed |
Collective Heavy Top Dynamics |
| title_sort |
collective heavy top dynamics |
| author |
Ohsawa, T. |
| author_facet |
Ohsawa, T. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We construct a Poisson map M: T*C² → se(3)* with respect to the canonical Poisson bracket on T*C² ≅ T*ℝ⁴ and the (−)-Lie-Poisson bracket on the dual se(3)* of the Lie algebra of the special Euclidean group SE(3). The essential part of this map is the momentum map associated with the cotangent lift of the natural right action of the semidirect product Lie group SU(2)⋉C² on C². This Poisson map gives rise to a canonical Hamiltonian system on T*C² whose solutions are mapped by M to solutions of the heavy top equations. We show that the Casimirs of the heavy top dynamics and the additional conserved quantity of the Lagrange top correspond to the Noether conserved quantities associated with certain symmetries of the canonical Hamiltonian system. We also construct a Lie-Poisson integrator for the heavy top dynamics by combining the Poisson map M with a simple symplectic integrator, and demonstrate that the integrator exhibits either exact or near conservation of the conserved quantities of the Kovalevskaya top.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210305 |
| citation_txt |
Collective Heavy Top Dynamics / T. Ohsawa // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 17 назв. — англ. |
| work_keys_str_mv |
AT ohsawat collectiveheavytopdynamics |
| first_indexed |
2025-12-07T21:25:05Z |
| last_indexed |
2025-12-07T21:25:05Z |
| _version_ |
1850886277789908992 |