Fraction of the radial velocity stable stars in the early observations of the Grid Giant Star Survey

The GGSS is a partially-filled, all-sky survey to identify K-giant stars with low level of RV-variability. We study histograms of the radial velocity (RV) variability obtained in the early phase of the Grid Giant Star Survey (GGSS, Bizyaev et al., 2006). This part of the survey has been conducted with a very limited nubmer of observations per star, and rough accuracy. We apply the Monte-Carlo simulations to infer a fraction of the RV-stable stars in the sample. Our optimistic estimate is that 20% of all considered K-giants have RV-variability under 30 m s$^{-1}$. Different assumptions of intrinsic RV-variability for our stars give 12 -- 20 % of RV-stable K-giants in the studied sample.Comment: 3 pages, 2 figures, to be published in PAS

Structural Parameters of Stellar Disks from 2MASS Images of Edge-on Galaxies

We present results of an analysis of the J, H, and K$_s$ 2MASS images of 139 spiral edge-on galaxies selected from the Revised Flat Galaxies Catalog. The basic structural parameters scalelength (h), scaleheight (z_0), and central surface brightness of the stellar disks (mu_0) are determined for all selected galaxies in the NIR bands. The mean relative ratios of the scaleheights of the thin stellar disks in the J:H:K$_s$ bands are 1.16:1.08:1.00, respectively. Comparing the scaleheights obtained from the NIR bands for the same objects, we estimate the scaleheights of the thin stellar disks corrected for the internal extinction. We find that the extinction-corrected scaleheight is, on average, 11% smaller than that in the K-band. Using the extinction-corrected structural parameters, we find that the dark-to-luminous mass ratio is, on average, 1.3 for the galaxies in our sample within the framework of a simplified galactic model. The relative thicknesses of the stellar disks z_0/h correlates with their face-on central surface brightnesses obtained from the 2MASS images. We also find that the scaleheight of the stellar disks shows no systematic growth with radius in most of our galaxies.Comment: To be published in Astrophysical Journa

On the Routh sphere problem

We discuss an embedding of a vector field for the nonholonomic Routh sphere into a subgroup of commuting Hamiltonian vector fields on six dimensional phase space. The corresponding Poisson brackets are reduced to the canonical Poisson brackets on the Lie algebra e(3). It allows us to relate nonholonomic Routh system with the Hamiltonian system on cotangent bundle to the sphere with canonical Poisson structure.Comment: LaTeX with AMSFonts, 11 page

The Hess-Appelrot system and its nonholonomic analogs

This paper is concerned with the nonholonomic Suslov problem and its generalization proposed by Chaplygin. The issue of the existence of an invariant measure with singular density (having singularities at some points of phase space) is discussed

Hamiltonization of Elementary Nonholonomic Systems

In this paper, we develop the Chaplygin reducing multiplier method; using this method, we obtain a conformally Hamiltonian representation for three nonholonomic systems, namely, for the nonholonomic oscillator, for the Heisenberg system, and for the Chaplygin sleigh. Furthermore, in the case of an oscillator and the nonholonomic Chaplygin sleigh, we show that the problem reduces to the study of motion of a mass point (in a potential field) on a plane and, in the case of the Heisenberg system, on the sphere. Moreover, we consider an example of a nonholonomic system (suggested by Blackall) to which one cannot apply the reducing multiplier method