2,763 research outputs found
Transitive decomposition of symmetry groups for the -body problem
Periodic and quasi-periodic orbits of the -body problem are critical
points of the action functional constrained to the Sobolev space of symmetric
loops. Variational methods yield collisionless orbits provided the group of
symmetries fulfills certain conditions (such as the \emph{rotating circle
property}). Here we generalize such conditions to more general group types and
show how to constructively classify all groups satisfying such hypothesis, by a
decomposition into irreducible transitive components. As examples we show
approximate trajectories of some of the resulting symmetric minimizers
On the dihedral n-body problem
Consider n=2l>=4 point particles with equal masses in space, subject to the
following symmetry constraint: at each instant they form an orbit of the
dihedral group D_l, where D_l is the group of order 2l generated by two
rotations of angle pi around two secant lines in space meeting at an angle of
pi/l. By adding a homogeneous gravitational (Newtonian) potential one finds a
special -body problem with three degrees of freedom, which is a kind of
generalisation of Devaney isosceles problem, in which all orbits have zero
angular momentum. In the paper we find all the central configurations and we
compute the dimension of the stable/unstable manifolds.Comment: Second version. In the first there was a mistake in a proof: some
section had been omitte
Stratified fibre bundles
A stratified bundle is a fibered space in which strata are classical bundles
and in which attachment of strata is controlled by a structure category of
fibers. Well known results on fibre bundles are shown to be true for stratified
bundles; namely the pull back theorem, the bundle theorem and the principal
bundle theorem.Comment: LaTeX file. Revised version. Accepted for publication on "Forum
Mathematicum
K-theory of stratified vector bundles
We show that the Atiyah-Hirzebruch K-theory of spaces admits a canonical
generalization for stratified spaces. For this we study algebraic constructions
on stratified vector bundles. In particular the tangent bundle of a stratified
manifold is such a stratified vector bundle.Comment: LaTeX file, 22 page
Time-resolved lidar fluorosensor for sea pollution detection
A contemporary time and spectral analysis of oil fluorescence is useful for the detection and the characterization of oil spills on the sea surface. Nevertheless the fluorosensor lidars, which were realized up to now, have only partial capability to perform this double analysis. The main difficulties are the high resolution required (of the order of 1 nanosecond) and the complexity of the detection system for the recording of a two-dimensional matrix of data for each laser pulse. An airborne system whose major specifications were: time range, 30 to 75 ns; time resolution, 1 ns; spectral range, 350 to 700 nm; and spectral resolution, 10 nm was designed and constructed. The designed system of a short pulse ultraviolet laser source and a streak camera based detector are described
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