The eigenvalues and eigenfunctions of a spherically symmetric anharmonic oscillator

We show that the operator H_s has a complete set of eigenfunctions and eigenvalues , which satisfy [2l(l + 1) - (3n² + 3n + 1)]s + o(s) and lim_s→0 = 0. The functions are given in spherical coordinates as a product of generalized Laguerre functions and spherical harmonics.     

Macroscopic energy diffusion for a chain of anharmonic oscillators

We study the energy diffusion in a chain of anharmonic oscillators where the Hamiltonian dynamics is perturbed by a local energy conserving noise. We prove that under diffusive rescaling of space–time, energy fluctuations diffuse and evolve following an infinite dimensional linear stochastic differential equation driven by the linearized heat equation. We also give variational expressions for the thermal diffusivity and some upper and lower bounds.     

非谐振子Gazeau-Klauder与Klauder-Perelomov相干态

利用Kinani-Daoud方法构造了非谐振子势的Gazeau-Klauder(GK)相干态和Klauder-Perelomov(KP)相干态，表明两种相干态在非线性谐振子势下具有完全不同的形式，并对两种相干态的完备性以及各自构成的Hilbert空间进行了讨论. 对相干态的Mandel Q参数的研究表明：GK相干态服从亚Poisson统计分布，KP相干态服从超Poisson统计分布.     

Wigner distribution functions for a relativistic linear oscillator

We construct the Wigner representation for a relativistic model of the linear harmonic oscillator governed by a finite-difference equation. We find Wigner functions for the stationary states, the thermodynamic equilibrium states, and the coherent states. We examine their nonrelativistic limits and the high and low temperature limits for the equilibrium states. We compute the mean values of the position and momentum coordinates for these Wigner functions. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 114, No. 3. pp. 410 425, March, 1998.     

Geometry of a five link mechanism with two degrees of freedom

The paper is devoted to the solution of straight and inverse geometrical tasks of five link mechanism with two degrees of freedom. The solution of the mentioned problem is very important in order to determine kinematic parameters of actuators. The problem can be divided into two parts. The first part is considered when we are given the coordinates of the output link of the mechanism and the necessity arises of determining the angles of rotation of actuators. On the other hand, it is very important to determine the position of the output link when the angles of rotation of the actuators are known. Here we consider that the mechanism is composed only of five classes of rotating kinematic pairs and the actuators are situated at the junctions of frames and links of the examined mechanism. The solution of the said problem is based on utilization of homogenous coordinates. On the basis of the obtained equations of motion, one can calculate the trajectories of motion of the output link as well angles of rotation of the actuators by taking into consideration preliminary given kinematic parameters of the mechanism. Here we also obtain equations for calculating values of speed and acceleration of the links of the mechanism. The calculations differ from known methods in simplicity and high performance, which would be useful for programming actuators mounted in the joints of the linkage.     

Hamiltonians with two degrees of freedom admitting a singlevalued general solution

Following the basic principles stated by Painleve, we first revisit the process of selecting the admissible time-independent Hamiltonians H=(p12 + p22)/2 + V(q1,q2) whose some integer power qjnj (t) of the general solution is a singlevalued function of the complex time t. In addition to the well known rational potentials V of Henon-Heiles, this selects possible cases with a trigonometric dependence of V on qj. Then, by establishing the relevant confluences, we restrict the question of the explicit integration of the seven (three "cubic" plus four "quartic") rational Henon-Heiles cases to the quartic cases. Finally, we perform the explicit integration of the quartic cases, thus proving that the seven rational cases have a meromorphic general solution explicitly given by a genus two hyperelliptic function.     

Kinetic model of the Boltzmann equation for a diatomic gas with rotational degrees of freedom

A system of model kinetic equations is proposed to describe flows of a diatomic rarefied gas (nitrogen). A conservative numerical method is developed for its solution. A shock wave structure in nitrogen is computed, and the results are compared with experimental data in a wide range of Mach numbers. The system of model kinetic equations is intended to compute complex-geometry three-dimensional flows of a diatomic gas with rotational degrees of freedom.     

A Factorization Theorem for Matrices over a Local Ring

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Buffer phenomenon in systems with one and a half degrees of freedom

The buffer phenomenon is established for some classical mechanics problems that are described by pendulum-type equations with time-periodic small additive terms. This phenomenon is as follows: the systems under consideration can have an arbitrary fixed number of stable periodic modes if the system parameters are properly chosen.     

Symmetric Cauchy stresses do not imply symmetric Biot strains in weak formulations of isotropic hyperelasticity with rotational degrees of freedom.

We show that symmetric Cauchy stresses do not imply symmetric Biot strains in relaxed weak formulations of finite isotropic hyperelasticity with exact rotational degrees of freedom. This is contrary to claims in the literature. It is noted that in the linear isotropic case with skew symmetric infinitesimal rotational degrees of freedom a similar discrepancy does not arise. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Forced oscillations of a viscoelastic system with a finite number of degrees of freedom

An exact solution is offered for the problem of forced oscillations of an arbitrary hereditary elastic system with a finite number of degrees of freedom.Moscow Institute of Electronic Engineering. Translated from Mekhanika Polimerov, No. 5, pp. 927–929, September–October, 1973.     

Orbit interpretation of Hamiltonian systems of the type of an anharmonic oscillator

An orbit (r-matrix) interpretation is offered in this paper for a recently constructed series of new integrable Hamiltonian systems with fourth-order potential of the type of an ariharmonic oscillator and a Garnier system.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 187–189, 1986.