On the motion of a reversible double simple pendulum with tracking force

Stability domains of a pendulum in the presence of tracking force and viscoelastic elements are constructed. It is shown that the boundary of the stability domains consists of sections of two hyperbolas. The effect of the pendulum parameters on the configuration of the stability domains is considered. Translated from Prikladnaya Mekhanika, Vol. 35, No. 7, pp. 108–112, July, 1999.     

Evolution of Limit Cycles in the Stability Domain of a Double Pendulum under a Variable Follower Force

It is shown that stable and unstable limit cycles are born at a certain value of the follower force. As the absolute value of the force increases, the cycles move with different velocities in opposite directions. The unstable limit cycle moves toward the origin in the four-dimensional phase space. At a certain value of the follower force, this cycle gets at the origin, disturbing its stability as a singular point of the dynamic system. If the absolute value of the follower force decreases, then death of both cycles is possible. In this case, the attraction domain of the origin becomes infinite     

Effect of medium pH on the optical properties of CdTe nanocrystals at colloidal synthesis and postsynthetic treatment

Physicochemical properties of low-dimensional structures based on CdTe obtained by colloidal synthesis method were studied. Effect of thioglycolic, hydroxyethylidenediphosphonic, and ethylenediaminetetraacetic acids as well as L-cysteine and thiourea on the processes of formation of CdTe nanocrystals in aqueous solutions was examined. Medium pH was shown to have a considerable effect on the process of their colloidal synthesis. The features of preparation of concentrated colloidal solutions of CdTe nanocrystals stabilized by thioglycolic acid and further sedimentational precipitation of monodisperse fractions from polydisperse solutions were studied. Optical absorption and photoluminescence spectra of the studied materials immediately after synthesis completion and after postsynthetic treatment were obtained and analyzed.     

Stability of equilibrium for an inverted two-link mathematical pendulum with critical tracking forces

We investigate nonlinear stability for equilibrium of a pendulum with viscoelastic components. The tracking force is chosen so that the matrix of the linearized part of the perturbed motion has two purely imaginary roots or one zero and one negative root. The other two roots are complex with negative real part. The boundary of the domain of stability is divided into “dangerous” and “safe” (in the sense of Bautin) zones. Translated from Prikladnaya Mekhanika, Vol. 35, No. 9, pp. 100–105, September, 1999.     

Effect of solvent nature on the stability of highly dispersed and nanosized cadmium telluride

Processes of adsorption modification of particle surface of disperse phase upon introduction of thioglycolic acid into highly dispersed systems based on CdTe were studied. It was shown that the selection of stabilizer composition and solvent enables purposeful effect on the properties of these systems. The stabilization of CdTe particles in highly dispersed and nanosized systems was found to be best conducted with the use of methanol and ethanol as a solvent. The postsynthetic treatment of colloidal solutions of CdTe nanocrystals with absolute ethyl alcohol was found to improve considerably their photoluminescent properties.     

Equilibrium of an Inverted Mathematical Double-Link Pendulum with a Follower Force

A discrete model of an elastic pendulum with a follower force is studied. This model is an inverted mathematical two-link pendulum with viscoelastic hinges. It is shown that divergent bifurcations are possible for some absolute values of the follower force and the stiffness of the restraint of the pendulum's upper end. As a result, the vertical position of the equilibrium becomes unstable and two new nonvertical stable equilibrium states (fork bifurcation) occur.