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- Miguel Rodríguez-Olmos, M. Esmeralda Sousa-Dias
- J. Nonlinear Science
- 2009

We apply geometric techniques to obtain the necessary and sufficient conditions on the existence and nonlinear stability of self-gravitating Riemann ellipsoids having at least two equal axes.

A method for testing Gμ-stability of relative equilibria in Hamiltonian systems of the form “kinetic + potential energy” is presented. This method extends the Reduced Energy-Momentum Method of Simo et al. to the case of non-free group actions and singular momentum values. A normal form for the symplectic matrix at a relative equilibrium is also obtained.

We obtain an algorithmic construction of the isotropy lattice for a lifted action of a Lie group G on TM and T ∗M based only on the knowledge of G and its action on M . Some applications to symplectic geometry are also shown.

We present a framework for the study of the local qualitative dynamics of equivariant Hamiltonian flows specially designed for points in phase space with nontrivial isotropy. This is based on the classical construction of structure-preserving tubular neighborhoods for Hamiltonian Lie group actions on symplectic manifolds. This framework is applied to… (More)

- Miguel C. Muñoz-Lecanda, Miguel Rodríguez-Olmos, M. Teixidó-Román
- J. Nonlinear Science
- 2015

We study the dynamics of a rigid body in a central gravitational field modeled as a Hamiltonian system with continuous rotational symmetries following the geometrical framework of Wang et al. Novelties of our work are the use the Reduced Energy Momentum for the stability analysis and the treatment of axisymmetric bodies. We explicitly show the existence of… (More)

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… (More)

We obtain a theory of stratified Sternberg spaces thereby extending the theory of cotangent bundle reduction for free actions to the singular case where the action on the base manifold consists of only one orbit type. We find that the symplectic reduced spaces are stratified topological fiber bundles over the cotangent bundle of the orbit space. We also… (More)

- OANA M. DRĂGULETE, TUDOR S. RATIU, MIGUEL RODRÍGUEZ-OLMOS, M. RODRÍGUEZ-OLMOS
- 2005

This paper studies singular contact reduction for cosphere bundles at the zero value of the momentum map. A stratification of the singular quotient, finer than the contact one and better adapted to the bundle structure of the problem, is obtained. The strata of this new stratification are a collection of cosphere bundles and coisotropic or Legendrian… (More)

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