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

Do Disk Galaxies with Abnormally Low Mass-to-Light Ratios Exist?

We performed the photometric B, V and R observations of nine disk galaxies that were suspected in having abnormally low total mass-to-light (M/L) ratios for their observed color indices. We use our surface photometry data to analyze the possible reasons for the anomalous M/L. We infer that in most cases this is a result of errors in photometry or rotational velocity, however for some galaxies we cannot exclude the real peculiarities of the galactic stellar population. The comparison of the photometric and dynamical mass estimates in the disk shows that the low M/L values for a given color of disks are probably real for a few our galaxies: NGC 4826 (Sab), NGC 5347 (Sab), and NGC 6814 (Sb). The small number of such galaxies suggests that the stellar initial mass function is indeed universal, and that only a small fraction of galaxies may have a non-typical low-mass star depleted initial mass function. Such galaxies require more careful studies for understanding their star formation history.Comment: 23 pages, 7 figures. This is a slightly shortened version of the paper published in Astronomy Letter

The portrait of Malin 2: a case study of a giant low surface brightness galaxy

The low surface brightness disc galaxy Malin2 challenges the standard theory of galaxy evolution by its enormous total mass ~2 10^12 Ms which must have been formed without recent major merger events. The aim of our work is to create a coherent picture of this exotic object by using the new optical multicolor photometric and spectroscopic observations at Apache Point Observatory as well as archival datasets from Gemini and wide-field surveys. We performed the Malin2 mass modelling, estimated the contribution of the host dark halo and found that it had acquired its low central density and the huge isothermal sphere core radius before the disc subsystem was formed. Our spectroscopic data analysis reveals complex kinematics of stars and gas in the very inner region. We measured the oxygen abundance in several clumps and concluded that the gas metallicity decreases from the solar value in the centre to a half of that at 20-30 kpc. We found a small satellite and measured its mass (1/500 of the host galaxy) and gas metallicity. One of the unique properties of Malin2 turned to be the apparent imbalance of ISM: the molecular gas is in excess with respect to the atomic gas for given values of the gas equilibrium turbulent pressure. We explain this imbalance by the presence of a significant portion of the dark gas not observable in CO and the Hi 21 cm lines. We also show that the depletion time of the observed molecular gas traced by CO is nearly the same as in normal galaxies. Our modelling of the UV-to-optical spectral energy distribution favours the exponentially declined SFH over a single-burst scenario. We argue that the massive and rarefied dark halo which had formed before the disc component well describes all the observed properties of Malin2 and there is no need to assume additional catastrophic scenarios proposed previously to explain the origin of giant LSB galaxies. [Abbreviated]Comment: 17 pages, 10 figures, accepted for publication in MNRA

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