Le problème des corps unidimensionnel et le mouvement rectiligne des gaz
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.
Linearization of nonholonomic systems at equilibrium points.
Measure-differential inclusions in percussional dynamics.
Mechanical oscillators with dampers defined by implicit constitutive relations
We study the vibrations of lumped parameter systems, the spring being defined by the classical linear constitutive relationship between the spring force and the elongation while the dashpot is described by a general implicit relationship between the damping force and the velocity. We prove global existence of solutions for the governing equations, and discuss conditions that the implicit relation satisfies that are sufficient for the uniqueness of solutions. We also present some counterexamples...
Mémoire sur la rotation de la lune
Mémoire sur le développement algébrique de la fonction perturbatrice.
Mémoire sur les équations du mouvement d'un système de corps.
Mémoire sur les inégalités séculaires des grands axes des orbites des planètes.
Minimization properties of Hill's orbits and applications to some N-body problems
Miss analysis in Lambert interceptions with application to a new guidance law.
Morse index properties of colliding solutions to the N-body problem
Motion of a particle submitted to dry friction and to normal percussions.
Motion with friction of a heavy particle on a manifold - applications to optimization
Let Φ : H → R be a C2 function on a real Hilbert space and ∑ ⊂ H x R the manifold defined by ∑ := Graph (Φ). We study the motion of a material point with unit mass, subjected to stay on Σ and which moves under the action of the gravity force (characterized by g>0), the reaction force and the friction force ( is the friction parameter). For any initial conditions at time t=0, we prove the existence of a trajectory x(.) defined on R+. We are then interested in the asymptotic behaviour of...
Motion with friction of a heavy particle on a manifold. Applications to optimization
Let be a function on a real Hilbert space and the manifold defined by Graph . We study the motion of a material point with unit mass, subjected to stay on and which moves under the action of the gravity force (characterized by ), the reaction force and the friction force ( is the friction parameter). For any initial conditions at time , we prove the existence of a trajectory defined on . We are then interested in the asymptotic behaviour of the trajectories when . More precisely,...
Motor-Mediated Microtubule Self-Organization in Dilute and Semi-Dilute Filament Solutions
We study molecular motor-induced microtubule self-organization in dilute and semi-dilute filament solutions. In the dilute case, we use a probabilistic model of microtubule interaction via molecular motors to investigate microtubule bundle dynamics. Microtubules are modeled as polar rods interacting through fully inelastic, binary collisions. Our model indicates that initially disordered systems of interacting rods exhibit an orientational instability...
Mouvement à un nombre fini de degrés de liberté avec contraintes unilatérales : cas avec perte d'énergie
Mouvement d'un projectile dans l'air
Mouvements relatifs à la surface de la terre
Multibump periodic motions of an infinite lattice of particles.