The Hess–Appelrot case and quantization of the rotation number

This paper is concerned with the Hess case in the Euler–Poisson equations and with its generalization on the pencil of Poisson brackets. It is shown that in this case the problem reduces to investigating the vector field on a torus and that the graph showing the dependence of the rotation number on parameters has horizontal segments (limit cycles) only for integer values of the rotation number. In addition, an example of a Hamiltonian system is given which possesses an invariant submanifold (similar to the Hess case), but on which the dependence of the rotation number on parameters is a Cantor ladder.     

Arylazopyrimidines as dichroic dyes for liquid crystals

Substituted 5-arylazopyrimidines and 2-arylazopyrimidines have been synthesized and investigated as dichroic dyes with positive dichroism, for liquid crystals. A promising series of 2-aryl-5-arylazopyrimidine dyes has been found, and a method is proposed for their synthesis by condensation of 2-aryl-5-aminopyrimidines with nitrosobenzenes in a superbasic medium.Deceased.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 209–214, February, 1993.     

Hamiltonicity and integrability of the Suslov problem

The Hamiltonian representation and integrability of the nonholonomic Suslov problem and its generalization suggested by S. A. Chaplygin are considered. This subject is important for understanding the qualitative features of the dynamics of this system, being in particular related to a nontrivial asymptotic behavior (i. e., to a certain scattering problem). A general approach based on studying a hierarchy in the dynamical behavior of nonholonomic systems is developed.     

The dynamics of a rigid body with a sharp edge in contact with an inclined surface in the presence of dry friction

In this paper we consider the dynamics of a rigid body with a sharp edge in contact with a rough plane. The body can move so that its contact point is fixed or slips or loses contact with the support. In this paper, the dynamics of the system is considered within three mechanical models which describe different regimes of motion. The boundaries of the domain of definition of each model are given, the possibility of transitions from one regime to another and their consistency with different coefficients of friction on the horizontal and inclined surfaces are discussed.     

Historical and critical review of the development of nonholonomic mechanics: the classical period

In this historical review we describe in detail the main stages of the development of nonholonomic mechanics starting from the work of Earnshaw and Ferrers to the monograph of Yu. I.Neimark and N.A. Fufaev. In the appendix to this review we discuss the d’Alembert–Lagrange principle in nonholonomic mechanics and permutation relations.     

Control of the motion of a helical body in a fluid using rotors

This paper is concerned with the motion of a helical body in an ideal fluid, which is controlled by rotating three internal rotors. It is proved that the motion of the body is always controllable by means of three rotors with noncoplanar axes of rotation. A condition whose satisfaction prevents controllability by means of two rotors is found. Control actions that allow the implementation of unbounded motion in an arbitrary direction are constructed. Conditions under which the motion of the body along an arbitrary smooth curve can be implemented by rotating the rotors are presented. For the optimal control problem, equations of sub-Riemannian geodesics on SE(3) are obtained.     

Oxygen diffusion in poly(methyl methacrylate) at low temperatures

Oxygen diffusion in atactic poly(methyl methacrylate) has been studied by anthracene luminescence quenching in geminate pairs anthracene-oxygen at 77–130 K. Analysis of the experimental data shows that the luminescence quenching is well accounted for by a polychromatic model assuming a log-normal diffusion coefficients distribution due to inhomogeneity of polymer structure. Energy activation is equal to 30 ± 1 KJ/mol. All diffusion coefficients data in the range 77–300 K demonstrate a good linear Arrhenius law. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 127–131, 1998     

Zur Frage der seitlichen Ionenstreuung bei der Implantation in amorphen und polykristallinen Festkörpern

The regularities of lateral scattering of ions in amorphous and polycrystal targets were derived. In contrary to well known LSS' method the proposed theoretical procedure enables to calculate root-mean-square deviations of ranges and lateral ranges for arbitrary ratios of target atom to ion masses within a wide range of energies from several MeV to energies near the binding energy of the atoms in solids. The theoretical estimates of root-mean square lateral deflection of ions are in good agreement with experimental results of different authors.