Stability of Hamiltonian relative equilibria
نویسندگان
چکیده
منابع مشابه
Stability of Poisson Equilibria and Hamiltonian Relative Equilibria by Energy Methods
We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum Methods. Using a topological generalisation of Lyapunov’s result that an extremal critical point of a conserved quantity is stable, we show that a Poisson equilibrium ...
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In the presence of noncompact symmetry, the stability of relative equilibria under momentum-preserving perturbations does not generally imply robust stability under momentum-changing perturbations. For axisymmetric relative equilibria of Hamiltonian systems with Euclidean symmetry, we investigate different mechanisms of stability: stability by energy-momentum confinement, KAM, and Nekhoroshev s...
متن کاملRelative equilibria in Hamiltonian systems: The dynamic interpretation of nonlinear stability on a reduced phase space
Stability of relative equilibria for Hamiltonian systems is generally equated with Liapunov stability of the corresponding fixed point of the flow on the reduced phase space. Under mild assumptions, a sharp interpretation of this stability is given in terms of concepts on the unreduced space. Suppose that (P, ω) is a symplectic manifold on which a Lie group G acts symplectically, and let H : P ...
متن کاملOn the Stability of Hamiltonian Relative Equilibria with Non-trivial Isotropy
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 [7] and by Lerman and Singer [3]. In both papers the authors give sufficient conditions for stability which require first determining a splitting of a subalgebra of g, with different splittings giving ...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 1999
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/12/3/315