Generalized Lagrange-d'Alembert Principle
Generalized polarized manifolds.
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 study of a family of integrable systems. (Étude géométrique d'une famille de systémes intégrables.)
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.
Géométrie des équations différentielles du second ordre
Geometrische Untersuchung über die Bewegung eines starren Körpers. Von Carl Neumann in Leipzig
Geometry of invariant tori of certain integrable systems with symmetry and an application to a nonholonomic system.
Hidden symmetries of the gravitational contact structure of the classical phase space of general relativistic test particle
The phase space of general relativistic test particle is defined as the 1-jet space of motions. A Lorentzian metric defines the canonical contact structure on the odd-dimensional phase space. In the paper we study infinitesimal symmetries of the gravitational contact phase structure which are not generated by spacetime infinitesimal symmetries, i.e. they are hidden symmetries. We prove that Killing multivector fields admit hidden symmetries of the gravitational contact phase structure and we give...
Hierarchy of integrable geodesic flows.
A family of integrable geodesic flows is obtained. Any such a family corresponds to a pair of geodesically equivalent metrics.
Homogenization of the transport equation describing convection-diffusion processes in a material with fine periodic structure
In the present contribution we discuss mathematical homogenization and numerical solution of the elliptic problem describing convection-diffusion processes in a material with fine periodic structure. Transport processes such as heat conduction or transport of contaminants through porous media are typically associated with convection-diffusion equations. It is well known that the application of the classical Galerkin finite element method is inappropriate in this case since the discrete solution...
Identification of quasiperiodic processes in the vicinity of the resonance
In nonlinear dynamical systems, strong quasiperiodic beating effects appear due to combination of self-excited and forced vibration. The presence of symmetric or asymmetric beatings indicates an exchange of energy between individual degrees of freedom of the model or by multiple close dominant frequencies. This effect is illustrated by the case of the van der Pol equation in the vicinity of resonance. The approximate analysis of these nonlinear effects uses the harmonic balance method and the multiple...
Infinitesimal symplectic relations and generalized hamiltonian dynamics
Internal properness and stability in linear systems
Isomorphism and Hamilton representation of some nonholonomic systems.
Jet bundle geometry, dynamical connections, and the inverse problem of lagrangian mechanics
Killing's equations in dimension two and systems of finite type
A PDE system is said to be of finite type if all possible derivatives at some order can be solved for in terms lower order derivatives. An algorithm for determining whether a system of finite type has solutions is outlined. The results are then applied to the problem of characterizing symmetric linear connections in two dimensions that possess homogeneous linear and quadratic integrals of motions, that is, solving Killing's equations of degree one and two.
L2 -characteristic classes of Maslov–Trofimov of hamiltonian systems on the Lie algebra of the upper-triangular matrices
We generalize the construction of Maslov-Trofimov characteristic classes to the case of some G-manifolds and use it to study certain hamiltonian systems.
La structure symplectique de la mécanique décrite par Lagrange en 1811