Gauge-independent Hamiltonian reduction of constrained systems.
General relativistic celestial mechanics of binary systems. II. The post-newtonian timing formula
Generalized Hamiltonian dynamics after Dirac and Tulczyjew
Dirac's generalized Hamiltonian dynamics is given an accurate geometric formulation as an implicit differential equation and is compared with Tulczyjew's formulation of dynamics. From the comparison it follows that Dirac's equation-unlike Tulczyjew's-fails to give a complete picture of the real laws of classical and relativistic dynamics.
Generalized Lagrange-d'Alembert Principle
Generalized polarized manifolds.
Generalized Whittaker's equations for holonomic mechanical systems.
Generic Nekhoroshev theory without small divisors
In this article, we present a new approach of Nekhoroshev’s theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems. The proof is an extension of a method introduced by P. Lochak, it combines averaging along periodic orbits with simultaneous Diophantine approximation and uses geometric arguments designed by the second author to handle generic integrable Hamiltonians. This method allows to deal with generic non-analytic Hamiltonians and to obtain new results of...
Geodesics in the compactly supported Hamiltonian diffeomorphism group.
Geodesics on quadrics and a mechanical problem of C. Neumann.
Geometric mechanics on nonholonomic submanifolds
In this survey article, nonholonomic mechanics is presented as a part of geometric mechanics. We follow a geometric setting where the constraint manifold is a submanifold in a jet bundle, and a nonholonomic system is modelled as an exterior differential system on the constraint manifold. The approach admits to apply coordinate independent methods, and is not limited to Lagrangian systems under linear constraints. The new methods apply to general (possibly nonconservative) mechanical systems subject...
Geometric quantization of the MIC-Kepler problem via extension of the phase space
Geometric structures associated with certain dynamical systems. (Structures géométriques associées à certains systèmes dynamiques.)
Geometric study of a family of integrable systems. (Étude géométrique d'une famille de systémes intégrables.)
Geometrical aspects of the covariant dynamics of higher order
We present some geometrical aspects of a higher-order jet bundle which is considered a suitable framework for the study of higher-order dynamics in continuous media. We generalize some results obtained by A. Vondra, [7]. These results lead to a description of the geometrical dynamics of higher order generated by regular equations.
Geometrical aspects of the Landau-Hall problem on the hiperbolic plane.
Se discuten algunos aspectos del problema de Landau-Hall hiperbólico. El álgebra de Lie de las simetrías infinitesimales de este problema se da explícitamente, resultando ser isomorfa a so(2,1) y que sus invariantes Noether asociados son los momentos angulares hiperbólicos. Asimismo se desarrolla la formulación hamiltoniana, lo que nos permitirá obtener la variedad de órbitas de energía constante de este problema mediante técnicas de reducción simpléctica.
Geometry of invariant tori of certain integrable systems with symmetry and an application to a nonholonomic system.
Geometry of non-holonomic diffusion
We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint distribution. For -Chaplygin systems, this yields a stochastic criterion for the existence of a smooth preserved measure. As an application of our results we consider the motion planning problem for the noisy two-wheeled robot and the noisy snakeboard.
Geometry of second-order connections and ordinary differential equations
The geometry of second-order systems of ordinary differential equations represented by -connections on the trivial bundle is studied. The formalism used, being completely utilizable within the framework of more general situations (partial equations), turns out to be of interest in confrontation with a traditional approach (semisprays), moreover, it amounts to certain new ideas and results. The paper is aimed at discussion on the interrelations between all types of connections having to do with...
Gli universi ipersferici, il gruppo conforme ed il campo gravitazionale di Newton.
Global existence and boundedness for quasi-variational systems.