87 citations · 877 across the 97 of their papers we have counts for
13 papers · 1 filter
Integrable systems in planar robotics
Tudor S. Ratiu, Nguyen Tien Zung
The main purpose of this paper is to investigate commuting flows and integrable systems on the configuration spaces of planar linkages. Our study leads to the definition of a natur…
Local normal forms of dynamical systems with a singular underlying geometric structure
Kai Jiang, Tudor S. Ratiu, Nguyen Tien Zung
In this paper we prove the existence of a simultaneous local normalization for couples , where is a vector field which vanishes at a point and is…
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…
Lagrangian reductions and integrable systems in condensed matter
François Gay-Balmaz, Michael Monastyrsky, Tudor S. Ratiu
We consider a general approach for the process of Lagrangian and Hamiltonian reduction by symmetries in chiral gauge models. This approach is used to show the complete integrabilit…
On the coupling between an ideal fluid and immersed particles
Henry O. Jacobs, Tudor S. Ratiu, Mathieu Desbrun
In this paper we use Lagrange-Poincare reduction to understand the coupling between a fluid and a set of Lagrangian particles that are supposed to simulate it. In particular, we re…
Symplectic bifurcation theory for integrable systems
Alvaro Pelayo, Tudor S. Ratiu, San Vu Ngoc
This paper develops a symplectic bifurcation theory for integrable systems in dimension four. We prove that if an integrable system has no hyperbolic singularities and its bifurcat…
Stability of equilibria for the free rigid body
Petre Birtea, Ioan Casu, Tudor S. Ratiu +1
The stability for all generic equilibria of the Lie-Poisson dynamics of the rigid body dynamics is completely determined. It is shown that for the generalized ri…
On the symmetry breaking phenomenon
Petre Birtea, Mircea Puta, Tudor S. Ratiu +1
We investigate the problem of symmetry breaking in the framework of dynamical systems with symmetry on a smooth manifold. Two cases will be analyzed: general and Hamiltonian dynami…
Asymptotic and Lyapunov stability of Poisson equilibria
Juan-Pablo Ortega, Víctor Planas-Bielsa, Tudor S. Ratiu
This paper includes results centered around three topics, all of them related with the nonlinear stability of equilibria in Poisson dynamical systems. Firstly, we prove an energy-C…
Symmetry breaking for toral actions in simple mechanical systems
Petre Birtea, Mircea Puta, Tudor S. Ratiu +1
For simple mechanical systems, bifurcating branches of relative equilibria with trivial symmetry from a given set of relative equilibria with toral symmetry are found. Lyapunov sta…
Singular reduction of implicit Hamiltonian systems
Guido Blankenstein, Tudor S. Ratiu
This paper develops the reduction theory of implicit Hamiltonian systems admitting a symmetry group at a singular value of the momentum map. The results naturally extend those know…
A short proof of chaos in an atmospheric system
Petre Birtea, Mircea Puta, Tudor S. Ratiu +1
We will prove the presence of chaotic motion in the Lorenz five-component atmospheric system model using the Melnikov function method developed by Holmes and Marsden for Hamiltonia…
Hamiltonian Hopf bifurcation with symmetry
Pascal Chossat, Juan-Pablo Ortega, Tudor S. Ratiu
In this paper we study the appearance of branches of relative periodic orbits in Hamiltonian Hopf bifurcation processes in the presence of compact symmetry groups that do not gener…