A qualitative investigation of the oscillations of a pendulum with a periodically varying length and a mathematical model of a swing

The behaviour of the amplitude-frequency characteristics of families of periodic solutions, produced from the equilibrium position of a system, is established by a qualitative investigation of the equation of the oscillations of a pendulum, the length of which is an arbitrary periodic function of time. The non-local conditions for their stability and instability, expressed in terms of the amplitude and frequency of the oscillations, are obtained. The results are used when discussing the parametric and self-excited oscillatory model of a swing. In the parametric model the length of a swing is a specified periodic function of time, and in the self-excited oscillatory model it is a function of the phase coordinates of the system. For an appropriate choice of these functions, both systems have a common periodic solution. It is shown that the parametric model leads to an erroneous conclusion regarding the instability of the periodic mode, which is in fact realized in the oscillations of a swing, whereas the self-excited oscillatory model indicates its stability.     

Possible mechanism of metal ion extraction from aqueous solutions by fibrous polypropylene

Peculiarities of the extraction of metal ions from aqueous solutions by fibrous polypropylene have been investigated. It has been found that metal ion adsorption proceeds owing to the existence of a gas-liquid-hydrophobic polymer boundary line. The process mechanism has been discussed.     

Mechanism of oxygen effect on hyrogenation rate of CO over palladium catalysts

Acceleration of CO hydrogenation by oxygen over palladium catalysts can be accounted for by competing reactions taking place in the CO-H₂O₂ system.

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, CO O₂ , CO–H₂–O₂.

     

Influence of oxygen on catalytic properties of supported palladium catalysts in CO hydrogenation

It has been established that the addition of oxygen to synthesis gas has a positive effect of the activity and selectivity of supported palladium catalysts in methanol synthesis. The degree of the effect of oxygen depends on the chemical nature of the support and the conditions of catalysis, preceding the addition of oxygen to the reaction mixture. The probable causes for the influence of oxygen on the catalytic properties of palladium, supported on oxide supports, have been discussed.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 25, No. 5, pp. 557–563, September–October, 1989.     

New polymer electrolyte membrane for medium-temperature fuel cell applications based on cross-linked polyimide Matrimid and hydrophobic protic ionic liquid

New hydrophobic protic ionic liquid, 2-butylaminoimidazolinium bis(trifluoromethylsulfonyl)imide (BAIM-TFSI), has been synthesized. The ionic liquid showed good thermal stability to at least 350 °C. The conductivity of BAIM-TFSI determined by electrochemical impedance method was found to be 5.6 × 10^?2 S/cm at 140 °C. Homogeneous composite films based on commercial polyimide (PI) Matrimid and BAIM-TFSI containing 30–60 wt% of ionic liquid were prepared by casting from methylene chloride solutions. Thermogravimetric analysis data indicated an excellent thermal stability of PI/BAIM-TFSI composites and thermal degradation points in the temperature range 377 °C–397 °C. The addition of ionic liquid up to 50 wt% in PI films does not lead to any significant deterioration of the tensile strength of the polymer. The dynamic mechanical analysis results indicated both an increase of storage modulus E′ of PI/BAIM-TFSI composites at room temperature and a significant E′ decrease with temperature compared with the neat polymer. The cross-linking of the PI with polyetheramine Jeffamine D-400 allowed to prepare PI/Jeffamine/BAIM-TFSI (50%) membrane with E′ value of 300 MPa at 130 °C. The ionic conductivity of this cross-linked composite membrane reached the level of 10^?2 S/cm at 130 °C, suggesting, therefore, its potential use in medium-temperature fuel cells operating in water-free conditions.     

Spatial distribution of RF radiation induced by cascade shower in lunar regolith

The results of calculation of the radiation pattern of an electron-photon shower induced by an ultrahigh-energy particle on the Moon’s surface are reported. It is found that the inclusion of dielectric characteristics of the lunar regolith radically changes the rf radiation intensity distribution at the vacuum-regolith interface.     

Coherent scattering of monochromatic RF radiation by ionization electrons of an extensive air shower

The possibility of detecting extensive air showers by recording and analyzing the radio pulse produced by the reradiation of a wave moving toward the cascade disk is considered. The coherent amplification of the scattered radiation in the direction of motion of the shower is shown to be due to a relativistic effect. An example of a real facility and its peculiarities are discussed.     

Stability of vertical oscillations in an electrodynamic suspension system with a discrete guideway structure

Conclusions 1. The coupling of the vehicle oscillation equation and the equations for the currents in the guideway structures must be taken into account in the stability analysis of vertical oscillations in an electrodynamic suspension system with a discrete guideway structure.2. The reported calculations indicate that vertical oscillations are unstable over a wide range of travel velocities. Consequently, the execution of steady-state vehicle motion requires vertical stabilization of the system.3. Effective stabilization can be achieved by means of a dynamic vibration damper. Even for a small relative mass =0.025 of the optimally tuned damper the perturbed motion decays rapidly.Physicotechnical Problems Branch of the Institute of Geotechnical Mechanics, National Academy of Sciences of Ukraine, Dnepropetrovsk. Translated from Prikladnaya Mekhanika, Vol. 31, No. 7, pp. 88–93, July, 1995.