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On the stability of Hamiltonian relative equilibria with non-trivial isotropy
- Publication Year :
- 2010
-
Abstract
- We consider Hamiltonian systems with symmetry, and relative equilibria with isotropy subgroup of positive dimension. The stability of such relative equilibria has been studied by Ortega and Ratiu and by Lerman and Singer. In both papers the authors give sufficient conditions for stability which require first determining a splitting of a subspace of the Lie algebra of the symmetry group, with different splittings giving different criteria. In this note we remove this splitting construction and so provide a more general and more easily computed criterion for stability. The result is also extended to apply to systems whose momentum map is not coadjoint equivariant.
- Subjects :
- Mathematics - Dynamical Systems
Mathematics - Symplectic Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1011.1130
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1088/0951-7715/24/10/007