On planar selfdual electroweak vortices
On singularities of Hamiltonian mappings
The notion of an implicit Hamiltonian system-an isotropic mapping H: M → (TM,ω̇) into the tangent bundle endowed with the symplectic structure defined by canonical morphism between tangent and cotangent bundles of M-is studied. The corank one singularities of such systems are classified. Their transversality conditions in the 1-jet space of isotropic mappings are described and the corresponding symplectically invariant algebras of Hamiltonian generating functions are calculated.
On some cohomological properties of the Lie algebra of Euclidean motions
The external derivative on differential manifolds inspires graded operators on complexes of spaces , , stated by dual to a Lie algebra . Cohomological properties of these operators are studied in the case of the Lie algebra of the Lie group of Euclidean motions.
On some completions of the space of hamiltonian maps
In one of his papers, C. Viterbo defined a distance on the set of Hamiltonian diffeomorphisms of endowed with the standard symplectic form . We study the completions of this space for the topology induced by Viterbo’s distance and some others derived from it, we study their different inclusions and give some of their properties. In particular, we give a convergence criterion for these distances that allows us to prove that the completions contain non-ordinary elements, as for example, discontinuous...
On some new treatment of artificial satellite's motion.
On stability problem of a top
On submanifolds and quotients of Poisson and Jacobi manifolds
We obtain conditions under which a submanifold of a Poisson manifold has an induced Poisson structure, which encompass both the Poisson submanifolds of A. Weinstein [21] and the Poisson structures on the phase space of a mechanical system with kinematic constraints of Van der Schaft and Maschke [20]. Generalizations of these results for submanifolds of a Jacobi manifold are briefly sketched.
On symmetries and constants of motion in Hamiltonian systems with nonholonomic constraints
On the algebraic structure on the jet prolongations of fibred manifolds
On the alpine ski with dry friction and air resistance. Some optimization problems for it
In the present work, divided in three parts, one considers a real skis-skier system, , descending along a straight-line with constant dry friction; and one schematizes it by a holonomic system , having any number of degrees of freedom and subjected to (non-ideal) constraints, partly one-sided. Thus, e.g., jumps and also «steps made with sliding skis» can be schematized by . Among the Lagrangian coordinates for two are the Cartesian coordinates and of its center of mass, , relative...
On the analytic non-integrability of the Rattleback problem
We establish the analytic non-integrability of the nonholonomic ellipsoidal rattleback model for a large class of parameter values. Our approach is based on the study of the monodromy group of the normal variational equations around a particular orbit. The imbedding of the equations of the heavy rigid body into the rattleback model is discussed.
On the application of control theory to certain problems for Lagrangian systems, and hyper-impulsive motion for these. I. Some general mathematical considerations on controllizable parameters
In applying control (or feedback) theory to (mechanic) Lagrangian systems, so far forces have been generally used as values of the control . However these values are those of a Lagrangian co-ordinate in various interesting problems with a scalar control , where this control is carried out physically by adding some frictionless constraints. This pushed the author to consider a typical Lagrangian system , referred to a system of Lagrangian co-ordinates, and to try and write some handy conditions,...
On the asymptotic behavior for a damped oscillator under a sublinear friction.
Mostramos la existencia de dos curvas de datos iniciales (x0, v0) para las cuales las soluciones x(t) correspondientes del problema de Cauchy asociado a la ecuación xtt + |xt|α-1 xt + x = 0, supuesto α ∈ (0,1), se anulan idénticamente después de un tiempo finito. Mediante métodos asintóticos y argumentos de comparación mostramos que para muchos otros datos iniciales las soluciones decaen a 0, en un tiempo infinito, como t-α / (1-α).
On The Atability Of Various Equilibrium And Stationary Motion Of Nonholonomic Systems
On The Canonical Formalisam With The Derivates Of Higher Order
On the canonical formalism with the derivatives of higher order.
On the characteristic modes of a rigid body under forces
On the classical non-integrability of the Hamiltonian system for hydrogen atoms in crossed electric and magnetic fields
Hydrogen atoms placed in external fields serve as a paradigm of a strongly coupled multidimensional Hamiltonian system. This system has been already very extensively studied, using experimental measurements and a wealth of theoretical methods. In this work, we apply the Morales-Ramis theory of non-integrability of Hamiltonian systems to the case of the hydrogen atom in perpendicular (crossed) static electric and magnetic uniform fields.
On the critical values of parametric resonance in Meissner's equation by the method of difference equations.
On the derivation of a first-order canonical set of hyperbolic Delaunay-type elements.