Differential equations with constraints in jet bundles: Lagrangian and Hamiltonian systems.
Discrete-continuous systems with symmetry.
Distinguished Riemann-Hamilton geometry in the polymomentum electrodynamics
In this paper we develop the distinguished (d-) Riemannian differential geometry (in the sense of d-connections, d-torsions, d-curvatures and some geometrical Maxwell-like and Einstein-like equations) for the polymomentum Hamiltonian which governs the multi-time electrodynamics.
Doubly asymptotic trajectories of Lagrangian systems and a problem by Kirchhoff
We consider Lagrangian systems with Lagrange functions which exhibit a quadratic time dependence. We prove the existence of infinitely many solutions tending, as , to an «equilibrium at infinity». This result is applied to the Kirchhoff problem of a heavy rigid body moving through a boundless incompressible ideal fluid, which is at rest at infinity and has zero vorticity.
Dynamical systems and Lagrangian spaces.
First integrals for two linearly coupled nonlinear Duffing oscillators.
Geodesics on quadrics and a mechanical problem of C. Neumann.
Geometric structures associated with certain dynamical systems. (Structures géométriques associées à certains systèmes dynamiques.)
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.
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...
Homoclinic orbits for an almost periodically forced singular Newtonian system in ℝ³
This work uses a variational approach to establish the existence of at least two homoclinic solutions for a family of singular Newtonian systems in ℝ³ which are subjected to almost periodic forcing in time variable.
Integrator for Lagrangian dynamics.
Inverse problem of the classical calculus of variations
Jet bundle geometry, dynamical connections, and the inverse problem of lagrangian mechanics
Lagrangian theory for presymplectic systems
Lie algebroids and mechanics
We give a formulation of certain types of mechanical systems using the structure of groupoid of the tangent and cotangent bundles to the configuration manifold ; the set of units is the zero section identified with the manifold . We study the Legendre transformation on Lie algebroids.
Mathematical model for diamond-type crystals with impurities or defects.
Mechanical Lagrangian systems with external forces.
Noether theorem and first integrals of constrained Lagrangean systems
The dynamics of singular Lagrangean systems is described by a distribution the rank of which is greater than one and may be non-constant. Consequently, these systems possess two kinds of conserved functions, namely, functions which are constant along extremals (constants of the motion), and functions which are constant on integral manifolds of the corresponding distribution (first integrals). It is known that with the help of the (First) Noether theorem one gets constants of the motion. In this...
Noether transformations with vanishing conserved quantity