30 citations · 147 across the 15 of their papers we have counts for
15 papers
Hamiltonian Relative Equilibria with Continuous Isotropy
James Montaldi, Miguel Rodriguez-Olmos
In symmetric Hamiltonian systems, relative equilibria usually arise in continuous families. The geometry of these families in the setting of free actions of the symmetry group is w…
Classification and stability of relative equilibria for the two-body problem in the hyperbolic space of dimension 2
Luis C. García-Naranjo, Juan C. Marrero, Ernesto Pérez-Chavela +1
We classify and analyze the stability of all relative equilibria for the two-body problem in the hyperbolic space of dimension 2 and we formulate our results in terms of the intrin…
The Fast-Superfast Transition in the Sleeping Lagrange Top
Tudor S. Ratiu, Miguel Rodriguez-Olmos, Miguel Teixidó-Román
The fast-superfast transition is a particular movement of eigenvalues found by Lewis et al. when studying the family of sleeping equilibria in the Lagrange top. Although this behav…
The Hamiltonian Tube Of A Cotangent-Lifted Action
Miguel Rodriguez-Olmos, Miguel Teixidó-Román
The Marle-Guillemin-Sternberg (MGS) form is local model for a neighborhood of an orbit of a Hamiltonian Lie group action on a symplectic manifold. One of the main features of the M…
A Hamiltonian Study Of The Stability and Bifurcations For The Satellite Problem
M. C. Muñoz-Lecanda, Miguel Rodriguez-Olmos, Miguel Teixidó-Román
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…
Reduction of a symplectic-like Lie algebroid with momentum map and its application to fiberwise linear Poisson structures
Juan Carlos Marrero, Edith Padron, Miguel Rodriguez-Olmos
This article addresses the problem of developing an extension of the Marsden- Weinstein reduction process to symplectic Lie algebroids, and in particular to the case of the symplec…
On the stability of Hamiltonian relative equilibria with non-trivial isotropy
James Montaldi, Miguel Rodriguez-Olmos
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 O…
Gauge equivalence and conserved quantities for Lagrangian systems on Lie algebroids
J. F. Cariñena, Miguel Rodriguez-Olmos
We develop a theory of gauge and dynamical equivalence for Lagrangian systems on Lie algebroids, also studying its relationship with Noether and non-Noether conserved quantities.
On Singular Poisson Sternberg Spaces
Matthew Perlmutter, Miguel Rodriguez-Olmos
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 mani…
Nonlinear Stability of Riemann Ellipsoids with Symmetric Configurations
Miguel Rodriguez-Olmos, M. Esmeralda Sousa-Dias
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…
Singular cosphere bundle reduction
Oana Dragulete, Tudor S. Ratiu, Miguel Rodriguez-Olmos
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…
Stability of relative equilibria with singular momentum values in simple mechanical systems
Miguel Rodriguez-Olmos
A method for testing -stability of relative equilibria in Hamiltonian systems of the form "kinetic + potential energy" is presented. This method extends the Reduced Energy-Mom…
The isotropy lattice of a lifted action
Miguel Rodriguez-Olmos
We obtain an algorithmic construction of the isotropy lattice for a lifted action of a Lie group on and based only on the knowledge of and its action on . So…
The Symplectic Normal Space of a Cotangent-Lifted Action
Matthew Perlmutter, Miguel Rodriguez-Olmos, M. Esmeralda Sousa-Dias
For the cotangent bundle of a smooth Riemannian manifold acted upon by the lift of a smooth and proper action by isometries of a Lie group, we characterize the symplectic normal sp…
On the geometry of reduced cotangent bundles at zero momentum
Matthew Perlmutter, Miguel Rodriguez-Olmos, M. Esmeralda Sousa-Dias
We consider the problem of cotangent bundle reduction for non free group actions at zero momentum. We show that in this context the symplectic stratification obtained by Sjamaar an…