Search results for "Names"
showing 10 items of 6843 documents
The tennis racket effect in a three-dimensional rigid body
2017
We propose a complete theoretical description of the tennis racket effect, which occurs in the free rotation of a three-dimensional rigid body. This effect is characterized by a flip ($\pi$- rotation) of the head of the racket when a full ($2\pi$) rotation around the unstable inertia axis is considered. We describe the asymptotics of the phenomenon and conclude about the robustness of this effect with respect to the values of the moments of inertia and the initial conditions of the dynamics. This shows the generality of this geometric property which can be found in a variety of rigid bodies. A simple analytical formula is derived to estimate the twisting effect in the general case. Differen…
Quasi-isometrically embedded subgroups of braid and diffeomorphism groups
2005
We show that a large class of right-angled Artin groups (in particular, those with planar complementary defining graph) can be embedded quasi-isometrically in pure braid groups and in the group of area preserving diffeomorphisms of the disk fixing the boundary (with respect to the $L^2$-norm metric); this extends results of Benaim and Gambaudo who gave quasi-isometric embeddings of $F\_n$ and $\Z^n$ for all $n>0$. As a consequence we are also able to embed a variety of Gromov hyperbolic groups quasi-isometrically in pure braid groups and in the diffeomorphism group of the disk. Examples include hyperbolic surface groups, some HNN-extensions of these along cyclic subgroups and the fundame…
Compressed Drinfeld associators
2004
Drinfeld associator is a key tool in computing the Kontsevich integral of knots. A Drinfeld associator is a series in two non-commuting variables, satisfying highly complicated algebraic equations - hexagon and pentagon. The logarithm of a Drinfeld associator lives in the Lie algbera L generated by the symbols a,b,c modulo [a,b]=[b,c]=[c,a]. The main result is a description of compressed associators that satisfy the compressed pentagon and hexagon in the quotient L/[[L,L],[L,L]]. The key ingredient is an explicit form of Campbell-Baker-Hausdorff formula in the case when all commutators commute.
On the classification of CAT(0) structures for the 4-string braid group
2005
This paper is concerned with the class of so-called CAT(0) groups, namely, those groups that admit a geometric (i.e., properly discontinuous, co-compact, and isometric) action on some CAT(0) space. More precisely, we are interested in knowing to what extent it is feasible to classify the geometric CAT(0) actions of a given group (up to, say, equivariant homothety of the space). A notable example of such a classification is the flat torus theorem, which implies that the minimal geometric CAT(0) actions of the free abelian group Z (n ≥ 1) are precisely the free actions by translations of Euclidean space E. Typically, however, a given group will have uncountably many nonequivalent actions, mak…
Finite index subgroups of mapping class groups
2011
Let g ≥ 3 and n ≥ 0, and let Mg,n be the mapping class group of a surface of genus g with n boundary components. We prove that Mg,n contains a unique subgroup of index 2g−1(2g − 1) up to conjugation, a unique subgroup of index 2g−1(2g + 1) up to conjugation, and the other proper subgroups ofMg,n are of index greater than 2g−1(2g+1). In particular, the minimum index for a proper subgroup of Mg,n is 2g−1(2g − 1). AMS Subject Classification. Primary: 57M99. Secondary: 20G40, 20E28. 0 Introduction and statement of results The interaction between mapping class groups and finite groups has long been a topic of interest. The famous Hurwitz bound of 1893 showed that the mapping class group of a clo…
Geodesic flow of the averaged controlled Kepler equation
2008
A normal form of the Riemannian metric arising when averaging the coplanar controlled Kepler equation is given. This metric is parameterized by two scalar invariants which encode its main properties. The restriction of the metric to $\SS^2$ is shown to be conformal to the flat metric on an oblate ellipsoid of revolution, and the associated conjugate locus is observed to be a deformation of the standard astroid. Though not complete because of a singularity in the space of ellipses, the metric has convexity properties that are expressed in terms of the aforementioned invariants, and related to surjectivity of the exponential mapping. Optimality properties of geodesics of the averaged controll…
Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
2007
Abstract This article deals with the optimal transfer of a satellite between Keplerian orbits using low propulsion and is based on preliminary results of Epenoy et al. (1997) where the optimal trajectories of the energy minimization problem are approximated using averaging techniques. The averaged Hamiltonian system is explicitly computed. It is related to a Riemannian problem whose distance is an approximation of the value function. The extremal curves are analyzed, proving that the system remains integrable in the coplanar case. It is also checked that the metric associated with coplanar transfers towards a circular orbit is flat. Smoothness of small Riemannian spheres ensures global opti…
Non subanalyticity of sub-Riemannian Martinet spheres
2001
Abstract Consider the sub-Riemannian Martinet structure (M,Δ,g) where M= R 3 , Δ= Ker ( d z− y 2 2 d x) and g is the general gradated metric of order 0 : g=(1+αy) 2 d x 2 +(1+βx+γy) 2 d y 2 . We prove that if α≠0 then the sub-Riemannian spheres S(0,r) with small radii are not subanalytic.
Convergence rate of a relaxed inertial proximal algorithm for convex minimization
2018
International audience; In a Hilbert space setting, the authors recently introduced a general class of relaxed inertial proximal algorithms that aim to solve monotone inclusions. In this paper, we specialize this study in the case of non-smooth convex minimization problems. We obtain convergence rates for values which have similarities with the results based on the Nesterov accelerated gradient method. The joint adjustment of inertia, relaxation and proximal terms plays a central role. In doing so, we highlight inertial proximal algorithms that converge for general monotone inclusions, and which, in the case of convex minimization, give fast convergence rates of values in the worst case.
Geometric and numerical techniques to compute conjugate and cut loci on Riemannian surfaces
2014
International audience; We combine geometric and numerical techniques - the Hampath code - to compute conjugate and cut loci on Riemannian surfaces using three test bed examples: ellipsoids of revolution, general ellipsoids, and metrics with singularities on S2 associated to spin dynamics.