The work attempts to analyze the scientific achievements of the St. Petersburg School of Mechanics in the field of rigid-body dynamics as a continuation of the review dedicated to the ...300th anniversary of St. Petersburg State University. This second part of the review describes a fifty-year period ending in 2023. It focuses on general theoretical research carried out by scientists from St. Petersburg State University on both uncontrolled and controlled motions of a rigid body.
This review, which consists of several works, is dedicated to the 300th anniversary of St. Petersburg State University (SPbSU) and is an attempt to analyze the scientific achievements of the St. ...Petersburg School of Mathematics and Mechanics in the field of rigid-body dynamics. This work, which is the first part of the review, covers the main achievements of the period from the founding of SPbSU to the mid-1970s. Due to the commemorative nature of this work, the scientific results obtained at SPbSU are considered in the context of events inextricably linked with the founding of the Academy of Sciences, the University and the gymnasium in 1724 and their further development over the subsequent 250 years. Due to the impossibility of covering even briefly all the publications that appeared during this period, attention is focused on the most important general areas of scientific thought and on those outstanding scientists of SPbSU, whose works enriched these areas.
The problem of attitude stabilization of a rigid body exposed to a nonstationary perturbing torque is investigated. The control torque consists of a restoring component and a dissipative one. Linear ...and nonlinear variants of restoring and perturbing torques are analyzed. Conditions of the asymptotic stability of the programmed orientation of the body are found with the use of the Lyapunov direct method and the averaging technique. The results of computer modeling, illustrating the conclusions obtained analytically, are presented.
The characteristics of acoustic-gravity waves (waveforms, time durations, amplitudes, azimuths and horizontal phase speeds) from the eruption of the Hunga-Tonga-Hunga-Hapai volcano detected at ...different infrasound stations of the Infrasound Monitoring System and at a network of low-frequency microbarographs in the Moscow region are studied. Using the correlation analysis of the signals at different locations, six arrivals of signals from the volcano, which made up to two revolutions around the Earth, were detected. The Lamb mode of acoustic gravity waves from the volcano eruption is identified and the effect of this mode on generation of tsunami waves and variation of aerosol concentration is studied. The energy released from an underwater volcano into the atmosphere is estimated from the parameters of the Lamb wave and compared with the energy released from the most powerful nuclear bomb of 58 Mt TNT.
Reflectometry and nonspecular (diffuse) X-ray scattering data are used to refine the structure parameters of planar multilayer films of saturated DPPC and DSPC phospholipids with thickness of about ...400 Å formed on the surface of an aqueous suspension of silica nanoparticles about 27 nm in diameter. A consistent analysis of the scattering data shows that the hydrosol–lipid film–air structure consists of a monolayer of nanoparticles, a lamellar lipid layer, and an approximately half-filled (loose) phospholipid monolayer at the air interface. Model electron concentration profiles indicate the hydration of the lamellar structure at a level of about 6 H
2
O molecules per lipid. In this case, water and Na
+
cations are localized in the region of phosphocholine groups, which is in agreement with the results of molecular dynamics calculations of other authors. The observed roughness of the interfaces between lipid layers is at least 5 Å and is indicative of the presence of a 3–6-Å-wide noncapillary-wave structure. In our opinion, one of the possible applications of the described technology is coating the concave surface of a rotating hydrosol liquid with a lipid multilayer in an X-ray deflecting device with a whispering gallery mode.
According to experimental data on X-ray scattering and reflectometry with synchrotron radiation, a twodimensional crystallization phase transition in a monolayer of melissic acid at the ...n-hexane–water interface with a decrease in the temperature occurs after a wetting transition.
The electric density profile along the normal to the phase interface between aromatic hydrocarbon toluene and water has been studied by X-ray reflectometry using synchrotron radiation. According to ...the experimental data, the width of the interface under normal conditions is (3.9 ± 0.1) Å. This value is much larger than a theoretical value of (5.7 ± 0.2) Å predicted by the theory of capillary waves with an interphase tension of (36.0 ± 0.1) mN/m. The observed broadening of the interface is attributed to its own diffuse near-surface structure with a width no less than Å, which is about the value previously discussed for (high-molecular-weight saturated hydrocarbon–water) and (1,2-dichloroethane–water) interfaces.
Without taking into account external friction, small transverse vibrations of a viscoelastic pipeline of unit length are described for nonnegative values of time in dimensionless variables by an ...integro-differential equation with hinged conditions at the ends and with initial conditions. The solution of this equation can be written in terms of an operator semigroup. In the present paper, we establish that this equation generates a semigroup that is analytic in some sector of the right half-plane.
PDF
