Editorial
Ehresmann Connection in the Geometry of Nonholonomic Systems
Eigenvalues of Killing tensors and separable webs on Riemannian and pseudo-Riemannian manifolds.
Eight-shaped Lissajous orbits in the Earth-Moon system
Euler and Lagrange proved the existence of five equilibrium points in the circular restricted three-body problem. These equilibrium points are known as the Lagrange points (Euler points or libration points) . The existence of families of periodic and quasi-periodic orbits around these points is well known (see [20, 21, 22, 23, 37]). Among them, halo orbits are 3-dimensional periodic orbits diffeomorphic to circles. They are the first kind of the so-called Lissajous orbits. To be selfcontained,...
Eine äquiaffine Charakterisierung der Cardan-Bewegung mittels der höheren Wendepole.
Eine neue partikuläre Lösung der Differentialgleichungen der Bewegung eines schweren starren Körpers um einen festen Punkt
Embedding set configuration spaces into those of Ruelle's point configurations
Energy and Momentum Conserving Methods of Arbitrary Order for the Numerical Integration of Equations of Motion. I. Motion of a Single Particle.
Energy Conserving, Arbitrary Order Numerical Solutions of the N-Body Problem.
Energy dissipation and hysteresis cycles in pre-sliding transients of kinetic friction
The problem of transient hysteresis cycles induced by the pre-sliding kinetic friction is relevant for analyzing the system dynamics, e.g., of micro- and nano-positioning instruments and devices and their controlled operation. The associated energy dissipation and consequent convergence of the state trajectories occur due to the structural hysteresis damping of contact surface asperities during reversals, and it is neither exponential (i.e., viscous type) nor finite-time (i.e., Coulomb type). In...
Entropy and complexity of a path in sub-riemannian geometry
We characterize the geometry of a path in a sub-riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset of a metric space is the minimum number of balls of a given radius needed to cover . It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We define the complexity of a path in a sub-riemannian manifold as the infimum of the lengths of all trajectories contained in an -neighborhood of the path,...
Entropy and complexity of a path in sub-Riemannian geometry
We characterize the geometry of a path in a sub-Riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset A of a metric space is the minimum number of balls of a given radius ε needed to cover A. It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We define the complexity of a path in a sub-Riemannian manifold as the infimum of the lengths of all trajectories contained in an ε-neighborhood of the path,...
Envelope construction of two-parameteric system of curves in the technological practice
A two-parametric system of close planar curves is defined in the introduction of the presented article. Next a theorem stating the existence of the envelope is presented and proved. A mathematical model of the collecting mechanism of the Horal forage trailer is developed and used for practical demonstrations. The collecting mechanism is a double joint system composed of three rods. An equation describing the trajectory of a random point of the working rod is derived using Maple. The trajectories...
Equations of motion of nonlinear nonholonomic systems with variable masses
Equilibrium configurations and small oscillations of some dynamical systems
Equilibrium stability of a servo actuating flight controls in a servoelastic framework.
Equivariance, variational principles, and the Feynman integral.
Errata : «Classification géométrique des structures internes des systèmes dynamiques à 2 spins»
Errata : “Generators for quasi-free completely positive semi-groups”
Erratum