DECOMPOSITION OF MULTIRATE DYNAMIC SYSTEMS WITH SMALL DISSIPATION

We consider singularly perturbed differential systems which describe the dynamics of manipulator with flexible joints in conditions of small dissipation. The existence of decoupling transformation which converts original multirate system to "block triangular" form with independent slow subsystem. Decoupling transformation is constructed as asymptotic series.

REDUCTION OF MATHEMATICAL MODEL OF ROBOT WITH ELASTIC JOINTS

A model of n - joint manipulator with elastic joints with small dissipation is studied. Class of singularly perturbed differential systems that describe the dynamics of robot is singled out. For a given class of systems the existence and uniqueness of integral manifoldness of slow movement is established, its features are studied. It is proved that integral manifold may be constructed with any degree of accuracy as asymptotic decomposition inpowers of small parameter. System that is used to describe movement in manifolds may be used as a reduced model of initial system.

Wave over the source in a thermal-conductive atmosphere

For acoustic-gravity waves, we propose a method for obtaining solutions over the source, taking into account the thermal conductivity throughout the atmosphere. The solution is constructed by combining the analytical solution for the upper isothermal part and numerical solution for the real non-isothermal dissipative atmosphere. The possibility of different ways of describing the wave disturbances investigated for different altitudinal ranges. A special way of accounting for small dissipation of the lower atmosphere is proposed. The heights of strong dissipation are found.

Long-term lidar observations of wintertime gravity wave activity over northern Sweden

This paper presents an analysis of gravity wave activity over northern Sweden as deduced from 18 years of wintertime lidar measurements at Esrange (68° N, 21° E). Gravity wave potential energy density (GWPED) was used to characterize the strength of gravity waves in the altitude regions 30–40 km and 40–50 km. The obtained values exceed previous observations reported in the literature. This is suggested to be due to Esrange's location downwind of the Scandinavian mountain range and due to differences in the various methods that are currently used to retrieve gravity wave parameters. The analysis method restricted the identification of the dominating vertical wavelengths to a range from 2 to 13 km. No preference was found for any wavelength in this window. Monthly mean values of GWPED show that most of the gravity waves' energy dissipates well below the stratopause and that higher altitude regions show only small dissipation rates of GWPED. Our analysis does not reproduce the previously reported negative trend in gravity wave activity over Esrange. The observed inter-annual variability of GWPED is connected to the occurrence of stratospheric warmings with generally lower wintertime mean GWPED during years with major stratospheric warmings. A bimodal GWPED occurrence frequency indicates that gravity wave activity at Esrange is affected by both ubiquitous wave sources and orographic forcing.

Comment on ‘Propagation of solitary waves and shock wavelength in the pair plasma (J. Plasma Phys. 78, 525–529, 2012)’

In a recent paper ‘Propagation of solitary waves and shock wavelength in the pair plasma (J. Plasma Phys. 78, 525–529, 2012)’, Malekolkalami and Mohammadi investigate nonlinear electrostatic solitary waves in a plasma comprising adiabatic electrons and positrons, and a stationary ion background. The paper contains two parts: First, the solitary wave properties are discussed through a pseudopotential approach, and then the influence of a small dissipation is intuitively sketched without theoretical underpinning. Small dissipation is claimed to lead to a shock wave whose wavelength is determined by linear oscillator analysis. Unfortunately, there are errors and inconsistencies in both the parts, and their combination is incoherent.