Orbitas Frenadas En Sistemas Mecanicos Finslerianos.
Oscillations presque-périodiques forcées d'équations d'Euler-Lagrange
Periodic solutions of quadratic lagrangian systems on -convex sets
Perturbations of Systems Describing the Motion of a Particle in Central Fields
The present paper deals with the KAM-theory conditions for systems describing the motion of a particle in central field.
Presymplectic lagrangian systems. II : the second-order equation problem
Reconstruction phases for Hamiltonian systems on cotangent bundles.
Réductibilité de systèmes dynamiques variationnels
Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite riemannian metric
For a riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the riemannian exponential...
Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric
For a Riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the Riemannian exponential...
Solving non-holonomic Lagrangian dynamics in terms of almost product structures.
Given a Lagrangian system with non-holonomic constraints we construct an almost product structure on the tangent bundle of the configuration manifold such that the projection of the Euler-Lagrange vector field gives the dynamics of the system. In a degenerate case, we develop a constraint algorithm which determines a final constraint submanifold where a completely consistent dynamics of the initial system exists.
Some results in Lagrangian mechanics
We associate to a dynamic equation three different connections and then we consider the meaning of the vanishing of their curvatures. Some peculiarities of the case of autonomous dynamic equation polynomial in the velocities are pointed out. Finally, using the so-called Helmholtz conditions, we investigate a particular example.
Sprays and homogeneous connections on
The homogeneity properties of two different families of geometric objects playing a crutial role in the non-autonomous first-order dynamics - semisprays and dynamical connections on - are studied. A natural correspondence between sprays and a special class of homogeneous connections is presented.
Structural discontinuities to approximate some optimization problems with a nonmonotone impulsive character
In some preceding works we consider a class of Boltz optimization problems for Lagrangian mechanical systems, where it is relevant a line , regarded as determined by its (variable) curvature function of domain . Assume that the problem is regular but has an impulsive monotone character in the sense that near each of some points to is monotone and is very large. In [10] we propose a procedure belonging to the theory of impulsive controls, in order to simplify into a structurally...
Sufficiency Conditions Under Which a Lagrangian is an Ordinary Divergence.
Sur le formalisme canonique pour les systèmes dégénérés.
Symmetries of a dynamical system represented by singular Lagrangians
Dynamical properties of singular Lagrangian systems differ from those of classical Lagrangians of the form . Even less is known about symmetries and conservation laws of such Lagrangians and of their corresponding actions. In this article we study symmetries and conservation laws of a concrete singular Lagrangian system interesting in physics. We solve the problem of determining all point symmetries of the Lagrangian and of its Euler-Lagrange form, i.e. of the action. It is known that every point...
Tensor fields defining a tangent bundle structure
The equivalence of controlled lagrangian and controlled hamiltonian systems
The purpose of this paper is to show that the method of controlled lagrangians and its hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...
The Equivalence of Controlled Lagrangian and Controlled Hamiltonian Systems
The purpose of this paper is to show that the method of controlled Lagrangians and its Hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying Lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...
The hamiltonian formalism in higher order variational problems