Nilpotentization of the kinematics of the n-trailer system at singular points and motion planning through the singular locus

We propose in this paper a constructive procedure that transforms locally, even at singular configurations, the kinematics of a car towing trailers into Kumpera-Ruiz normal form. This construction converts the nonholonomic motion planning problem into an algebraic problem (the resolution of a system of polynomial equations), which we illustrate by steering the two-trailer system in a neighborhood of singular configurations. We show also that the n-trailer system is a universal local model for all Goursat structures and that all Goursat structures are locally nilpotentizable.Comment: LaTeX2e, 23 pages, 4 figures, submitted to International journal of contro

Contact systems and corank one involutive subdistributions

We give necessary and sufficient geometric conditions for a distribution (or a Pfaffian system) to be locally equivalent to the canonical contact system on Jn(R,Rm), the space of n-jets of maps from R into Rm. We study the geometry of that class of systems, in particular, the existence of corank one involutive subdistributions. We also distinguish regular points, at which the system is equivalent to the canonical contact system, and singular points, at which we propose a new normal form that generalizes the canonical contact system on Jn(R,Rm) in a way analogous to that how Kumpera-Ruiz normal form generalizes the canonical contact system on Jn(R,R), which is also called Goursat normal form.Comment: LaTeX2e, 29 pages, submitted to Acta applicandae mathematica

A Census of White Dwarfs Within 40 Parsecs of the Sun

Our aim is to compile a catalog of white dwarfs within 40 parsecs of the Sun, in which newly discovered objects would significantly increase the completeness of the current census. White dwarf candidates are identified from the SUPERBLINK proper motion database (Lepine & Shara 2005), which allows us to investigate stars down to a proper motion limit as low as 40 mas yr-1. The selection criteria and distance estimates are based on a combination of color-magnitude and reduced proper motion diagrams. Candidates with distances less than 50 parsecs are selected for spectroscopic follow-up. We present our preliminary sample of spectroscopically confirmed white dwarfs, as well as their atmospheric parameters. These parameters are obtained using the spectroscopic technique developed in Bergeron et al.(1992) for DA stars. DB, DQ, and DZ stars are also analyzed spectroscopically. For featureless spectra as well as those showing only Halpha, we perform a detailed photometric analysis of their energy distribution.Comment: 4 pages, 3 figures, to appear in AIP Conference Proceedings for the 17th European White Dwarf Worksho

The Effect of Corotation on the Radial Gradient of Metallicity of Spiral Galaxies

The corotation radius in a spiral galaxy is the radius where the spiral pattern speed has the same velocity of the rotation curve. By compiling results from the literature for 20 spiral galaxies we verified a strong correlation between the radius of the minima or inflections of the metallicity distribution and the corotation radius.Comment: 3 pages, 1 figur